Foundations of Physics Blackline Masters. Credits

Transcription

1 Foundations of Physics Blackline Masters Credits CPO Science Curriculum Development Team Author: Thomas Hsu, Ph.D Vice Presidents: Thomas Narro and Lynda Pennell Writers: Stacy Kissel, Lainie Ives, Mary Beth Hughes, Sonja Taylor and Scott Eddleman Graphic Artists: Bruce Holloway and Polly Crisman Technical Consultants Tracy Morrow, Julie Dalton, and Mary Ann Erickson Foundations of Physics Blackline Masters Copyright 2004 CPO Science All rights reserved. No part of this work may be reproduced or transmitted in any form or by an means, electronic or mechanical, including photocopying and recording, or by any information store or retrieval system, without permission in writing. For permission and other rights under this copyright, please contact: CPO Science 26 Howley Street, Peabody, MA (866) cpo.com Printed and Bound in the United States of America

2 Blackline Masters Blackline Masters are designed to be used as answer sheets for the Investigations. Students should use their Investigations Manual to read, follow procedures, and look at diagrams. They should record answers to questions, data, and make graphs using the Blackline Masters. 2.1 Distance and Length 2.2 Time 2.3 Mass, Matter, and the Atom 3.1 Speed 3.2 Observations of Motion 3.3 Analyzing Motion with Graphs 4.1 Acceleration 4.2 A Model for Accelerated Motion 4.3 Free Fall and the Acceleration due to Gravity 5.1 The First Law: Force and Inertia 5.2 The Second Law: Force, Mass, and Acceleration 5.3 The Third Law: Action and Reaction 6.1 Mass, Weight and Gravity 6.2 Friction 6.3 Equilibrium of Forces and Hooke s Law 7.1 Vectors and Direction 7.2 Projectile Motion and the Velocity Vector 7.3 Forces in Two Dimensions 8.1 Motion in Circles 8.2 Centripetal Force 8.3 Universal Gravitation and Orbital Motion 9.1 Torque 9.2 Center of Mass 9.3 Rotational Inertia 10.1 Machines and Mechanical Advantage 10.2 Work 10.3 Energy and Conservation of Energy 11.1 Efficiency 11.2 Energy and Power 11.3 Energy Flow in Systems 12.1 Momentum 12.3 Angular Momentum 13.1 Harmonic Motion 13.2 Why Things Oscillate 13.3 Resonance and Energy 14.1 Waves and Wave Pulses 14.2 Motion and Interaction of Waves 14.3 Natural Frequency and Resonance 15.1 Properties of Sound 15.2 Sound Waves 15.3 Sound, Perception, and Music 16.1 Properties and Sources of Light 16.2 Color and Vision 16.3 Photons and Atoms 17.1 Reflection and Refraction 17.2 Mirrors, Lenses and Images 17.3 Optical Systems 18.1 The Electromagnetic Spectrum 18.2 Interference, Diffraction, and Polarization 18.3 Special Relativity 19.1 Electric Circuits 19.2 Current and Voltage 19.3 Electrical Resistance and Ohm s Law 20.1 Series and Parallel Circuits 20.2 Analysis of Circuits 20.3 Electric Power, AC, and DC Electricity 21.1 Electric Charge 21.2 Coulomb s Law 21.3 Capacitors 22.1 Properties of Magnets 22.2 Magnetic Properties of Materials 22.3 The Magnetic Field of the Earth 23.1 Electric Current and Magnetism 23.2 Electromagnets and the Electric Motor 23.3 Induction and the Electric Generator 24.1 Semiconductors 24.2 Circuits with Diodes and Transistors 24.3 Digital Electronics 25.1 Matter and Atoms 25.2 Temperature and the Phases of Matter 25.3 Heat and Thermal Energy 26.1 Heat Conduction 26.2 Convection 26.3 Radiant Heat 27.1 Properties of Solids 27.2 Properties of Liquids and Fluids 27.3 Properties of Gases 28.1 The Nucleus and Structure of the Atom 28.2 Electrons and Quantum States 28.3 The Quantum Theory 29.1 Chemistry 29.2 Chemical Bonds 29.3 Chemical Reactions 30.1 Radioactivity 30.2 Radiation 30.3 Nuclear Reactions and Energy Note: All formulas used in the text are found on the sheets at the back of this file. These sheets can be copied for student use.

3 Name: 2.1 Distance and Length A Question: How do we accurately communicate length and distance? Estimating a. Look at a meter stick but do not use it to measure anything yet. Imagine holding a meter stick up to your body. Estimate your height in meters. b. Use the meter stick to measure your height in meters. How far off was your estimate compared with the actual measurement? Express your answer as a percent of your actual height. B Estimate lengths and distances in meters Use your sense of how long a meter is to estimate the following lengths. a. The length of your classroom. b. The diameter of your pencil s eraser. c. The height of your desk or laboratory bench. d. The length of a paper clip. e. The distance from where you live to this lab or classroom. C Significant digits and measuring length Measure and record each length using the proper number of significant figures. 1. The length of your classroom. 2. The diameter of your pencil s eraser. 3. The height of your desk or laboratory bench. 4. The length of a paper clip. 5. The length of your physics textbook. D Analyzing the results a. Which estimate was closer to the actual measurement, the length of a paper clip or the length of your lab or classroom? Can you think of why? Answer Sheet 2.1 Distance and Length

4 b. Use a map to estimate the distance from your school or lab to your home. Next time you travel from your home to school, use the car s (or bicycle s) odometer to measure the distance. Compare the measurement with your estimate. E Area a. Calculate the area of one side of a sheet of paper in square inches. b. Convert the length and width measurements from inches to meters. c. Calculate the area in square meters. Hint: The answer is much less than 1 m 2. d. Estimate the area of the floor of your lab or classroom. e. How many sheets of paper would it take to cover the floor of your lab or classroom? Explain how you arrived at your estimate, and show any calculations you made. 2.1 Distance and Length Answer Sheet

5 F Volume a. How many liters fit in a cube that is 30 centimeters on a side? b. Calculate the volume of a cylinder that has a radius of 4 centimeters and a height of 20 centimeters. The volume of a cylinder is approximately 3.14 radius radius height. This relationship is often written V = πr 2 h. How many liters fit in this cylinder? G Volume by experiment a. Calculate the height of a cylinder that has a radius (r) of 4 centimeters and a volume of 1,000 cm 3. (Hint: The volume of a cylinder is πr 2 h.) b. How close did 1 liter of sand come to matching the height required to make a volume of 1,000 cm 3? Answer Sheet 2.1 Distance and Length

6 Extra space for notes and performing calculations: 2.1 Distance and Length Answer Sheet

7 Name: 2.2 Time Question: How do we measure and describe time? A Using the Timer as a stopwatch There are no questions to answer in Part 1. B Mixed units for time a. Arrange the following three time intervals from shortest to longest: 1) 4 hours, 23 minutes and 15 seconds (4:23:15) 2) 250 minutes 3) 16,000 seconds C Using the photogates a. Exactly what action do you take to start and stop the Timer? Be very specific in your answer. Someone who has never seen the photogate before should be able to read your answer and know what to do with the light beam to make the Timer start, and what to do to make it stop. b. If you block the light beam several times in a row, does the Timer add each new measurement to the last one or does it start at zero every time you break the beam? Your answer should provide observations that back up what you say. Answer Sheet 2.2 Time

8 D Using the Timer with two photogates a. What starts and stops the Timer when only the A light is on? b. What starts and stops the Timer when only the B light is on? c. What starts and stops the Timer when both A and B lights are on? d. Does the Timer still make measurements when there are no lights on? e. What happens if you go though photogate A once and through photogate B multiple times? When answering this question, you might want to think about a race where all the runners start together but you want each runner s individual time for finishing the race. E Accuracy, resolution and precision a. Resolution means the smallest interval that can be measured. Try using one photogate to determine the resolution of the Timer. Give your answer in seconds and tell how your observations support your answer. 2.2 Time Answer Sheet

9 b. The word accuracy refers to how close a measurement is to the true value. Which of the following statements best describes what you know about the accuracy of time measurements made with the photogates? Give a reason for your answer. 1. The Timer is accurate to seconds. 2. The Timer is accurate to seconds. 3. It is impossible to know the accuracy without more information on how the Timer determines one second. 4. A time of seconds is more accurate than a time of 26 seconds. c. The word precision describes how closely repeated measurements of the same quantity can be made. When measurements are very precise, they are close to the same value. For example, an ordinary clock (with hands) can determine the time to a precision of about a second. That means many people reading the same clock at the same time will read times that are within a second of each other. It is possible to be precise but not accurate. Which is likely to be more precise: time measurements made with a stopwatch or measurements made with photogates? Answer Sheet 2.2 Time

10 Extra space for notes and performing calculations: 2.2 Time Answer Sheet

11 Name: 2.3 Mass, Matter, and the Atom A Question: How is mass described? Estimating mass a. Pick up a full (1 liter) bottle of soda to get a sense of the amount of mass in a kilogram. Next, pick up a book such as your textbook. Use the comparison to estimate the mass of the book in kilograms. B C D Estimate the mass of each object: Estimate the mass of the following objects in kilograms: a. Your pencil. b. Your shoe. c. A cement block. d. Yourself. e. An automobile. f. A paper clip. Measuring Mass a. Use the appropriate measuring device to measure the mass in kilograms of each object below: Your pencil. Your shoe. A cement block. Yourself. An automobile. A paper clip. Scientific notation a. Rewrite your estimates from 2a - 2f using scientific notation. Your pencil. Your shoe. A cement block. Yourself. An automobile. A paper clip. Answer Sheet 2.3 Mass, Matter, and the Atom

12 a. Look up or estimate the mass of each of these objects and write it both using scientific notation and as a decimal (ordinary) number. It is difficult to write some of the masses as decimal (ordinary) numbers. a An atom of hydrogen. b An atom of uranium. c A grain of sand. d The space shuttle. e An official professional soccer ball. f The planet Earth. 2.3 Mass, Matter, and the Atom Answer Sheet

13 Name: 3.1 Speed Question: What is speed and how is it measured? A Calculating the speed of the rolling ball Table 1: Speed, Distance, and Time Data Distance from A to B Time from A to B (sec) Speed (feet) (ft/sec) (centimeters) (cm/sec) (inches) (in/sec) (meters) (m/sec) a. Calculate the speed of the ball in ft/sec, cm/sec, in/sec, and m/sec, and write the results in the table. b. Which is the fastest speed of the four or are they all the same speed? c. Is it possible that a speed of 254 and a speed of 100 could be the same speed? Explain your answer, and and state why a speed as 254 is not a very good answer. B Relationships between distance, speed, and time There are no questions to answer in Part 2. C Setting up a controlled speed Distance between photogates (m): Required time from A to B (calculated, sec): Actual time from A to B (measured, sec): Actual speed (calculated, m/sec): Answer Sheet 3.1 Speed

14 a. How did you make the time between photogates longer? b. How did you make the time between photogates shorter? c. Calculate the percent difference between your measured speed and 1 meter per second. 3.1 Speed Answer Sheet

15 Name: 3.2 Observations of Motion A Question: Can you predict the speed of a ball rolling down a ramp? Setting up an experiment a. Look around the class and note which hole each group is using for its track. With your group, make a prediction as to which track will have the fastest ball. b. Roll the ball down the track and record the time it takes to go from photogate A to photogate B. c. Compare your results with other groups. Did the times that everyone measured agree with your hypothesis about how the angle of the track would affect the ball s speed? Why or why not? d. Is there a better way to test whether increasing the ramp angle makes the ball go faster? Explain how you would redo this experiment so the results make sense. B Variables in an experiment a. What variables may affect the time it takes the ball to get from photogate A to photogate B? Use Table 1 to list all the variables discussed by your group, or by the class. Table 1: Variables that affect the time between photogates Variable Variable C Doing a controlled experiment Table 2: Variables and values for a controlled experiment Variable Value Variable Value Once you have your new results, compare them with the results of the other groups. Answer Sheet 3.2 Observations of Motion

16 a. Did your times agree with your hypothesis of how they would change with the angle of the track? b. In one or two sentences describe why this experiment was better or worse than your first experiment. Your answer should discuss the cause-and-effect relationships and variables. c. It is often easy to confuse cause and effect. When we see something happen, we think up a reason for it happening but we do not always get the right reason. If you drop a piece of paper and a steel weight at the same time, which one hits the ground first? If the paper is flat, the steel weight always hits first. Why does the steel weight hit first? Is it because heavier objects fall faster, or is there another reason? In your answer, give at least one other reason a steel weight might fall faster than a flat sheet of paper. D Finding the speed of the ball at different points along the track Table 3: Speed, position, and time data Position of photogate A (cm) from top of track Time from photogate A (sec) Distance traveled by the ball (1.9 cm) Speed of the ball (cm/sec) 3.2 Observations of Motion Answer Sheet

17 E Graphing and analyzing the results a. Do you notice a trend in your measurements? Does the speed of the ball change as it moves down? b. Graph the speed of the ball versus its position. Place speed of the ball on the y-axis and position of photogate A on the x-axis. Add labels to each axis and title the graph. c. What does the graph show about the speed of the ball? Answer Sheet 3.2 Observations of Motion

18 F Using your graph to predict the speed of the ball a. Choose a spot on the track where you did not measure the speed of the ball. b. Use your graph to find the predicted speed of the ball at that position. Record your predicted speed. c. Use the speed formula to calculate the time it should take the ball to pass through the light beam at the predicted speed. For example, if the ball were going 100 centimeters per second, it would take.0190 seconds to pass through the beam (1.9 cm 100 cm/sec =.0190 sec). d. Place the photogate at the spot on the track you chose in step (a) and record the time it takes for the ball to pass through the photogate. e. How does the predicted time compare with the actual measured time? What does this tell you about your experiment and measurements? G Calculating percent error a. Find the difference between the predicted time and the actual measured time. Predicted time Actual time = Difference b. Take this difference and divide it by the predicted speed and then multiply by 100. ( Difference Predicted time) 100 = Percent error c. Use the percent error to calculate percent correct. 100 Percent error = Percent correct 3.2 Observations of Motion Answer Sheet

19 Name: 3.3 Analyzing Motion with Graphs A Question: How do you model motion? Setting up the experiment a. Suppose the ball takes a longer time to pass through photogate B compared with photogate A. Should you raise or lower the catcher end to bring the times closer together? b. After you get the track as level as you can, calculate the speed of the ball as it passes through each photogate. Remember, speed is the diameter (1.9 centimeters) divided by the time through the photogate. How close are the two speeds? Express your answer as a percentage of the speed through photogate A. For example, the speed at B might be 1 percent slower than the speed at A. B C Measuring the motion of the ball Record the data in Table 1. Recording your data in Table 1 Table 1: Position, Speed, and Time Data x (cm) t AB (sec) t A (sec) t B (sec) v A (cm/sec) v B (cm/sec) Answer Sheet 3.3 Analyzing Motion with Graphs

20 D Graphing and analyzing your data a. Make a position versus time graph using your data. Plot the time from A to B on the x-axis and the position from A to B (position of photogate B) on the y-axis. At this point, do not connect the data points on the graph. Be sure to label the axes and title the graph. b. Is the graph a straight line or a curve? c. Does the graph get steeper as the ball rolls farther, or does the graph keep the same slope the whole way? What does your answer tell you about the speed of the ball at different times as it rolls along the track? d. Draw a triangle on your graph and determine the rise and run from the triangle (see diagram). Calculate the speed from the slope of the graph. Is the value you get consistent with other speed measurements you have made with the ball and track? 3.3 Analyzing Motion with Graphs Answer Sheet

21 E The speed versus time graph a. Make a graph of speed versus time. Speed should be the speed at photogate B (v B ) since photogate B was the one that moved. Time should be the time from A to B (t AB ). Put speed on the y-axis since it is the dependent variable. Time goes on the x-axis because it is the independent variable. b. Describe the graph; does it slope up or down? Is it level or nearly level? Is it a line or a curve? c. Remember, the distance traveled is the product of speed and time. Think about a rectangle drawn on the speed versus time graph. The width of the rectangle is the time. The height of the rectangle is the speed. Since area is width height, the area on the speed versus time graph is the distance traveled. Pick two times that correspond to measurements that are not right next to each other. Draw the rectangle that lies between the x-axis, the line showing speed, and the two times you chose. Calculate the area of the rectangle. It should be the same as the distance between the two positions of photogate B. Answer Sheet 3.3 Analyzing Motion with Graphs

22 Extra space for notes and performing calculations: 3.3 Analyzing Motion with Graphs Answer Sheet

23 Name: 4.1 Acceleration Question: How is the speed of the ball changing? A Setting up Table 1: Acceleration Data t A : time through A (sec) t B : time through B (sec) t AB : time A to B (sec) v A : speed at A (sec) v B : speed at B (sec) a: acceleration (sec) Trial 1 Trial 2 Trial 3 B Looking at the data a. If you moved the photogates to different places, the speeds for each of the three trials should be different from each other. Are the accelerations different? If so, by how much are they different between the three trials? b. What would the acceleration be if you pushed the ball at the start? Would you expect it to be greater, less, or about the same compared with the acceleration you measured without pushing? Answer the question and then try it. You can give the ball a small push by rolling lightly with your finger at the start. NOTE: Measure the acceleration a distance away from the start, so your finger does not get in the way. c. Propose at least one way to increase the acceleration of the ball on the track. C The speed versus time graph Record the data in Table 1. Answer Sheet 4.1 Acceleration

24 D Recording position, speed, and time data in Table 2 Table 2: Position, speed, and time data x (cm) t AB (sec) t A (sec) t B (sec) v A (cm/sec) v B (cm/sec) E Graphing speed versus time a. Make a speed versus time graph. Plot the speed at photogate B on the y-axis. Plot the time from A to B on the x-axis. 4.1 Acceleration Answer Sheet

25 b. Is your graph a straight line or a curve? c. The place on the speed versus time graph where the line crosses the y-axis is called the y-intercept. The y-intercept represents something about the ball. What does the y-intercept of your speed versus time graph represent? (Hint: The y-axis is speed.) d. Does the ball accelerate as it rolls down the track? Justify your answer. Remember that acceleration is defined as a change in speed over time. F Calculating acceleration from the slope of the line a. Using your speed versus time graph, calculate the acceleration of the ball from the slope of the line. b. How does the acceleration from the slope compare with the acceleration you calculated from the times in Part 1 of the Investigation? c. Is the acceleration of the ball changing as it moves down the track? Explain your answer using what you know about the slope of a straight line. Answer Sheet 4.1 Acceleration

26 Extra space for notes and performing calculations: 4.1 Acceleration Answer Sheet

27 Name: 4.2 A Model for Accelerated Motion Question: How do we describe and predict accelerated motion? A The equations for accelerated motion in a line There are no questions to answer in Part 1. B Planning the experiment a. Write down the equations for uniform accelerated motion in one dimension using the following variables. Let: t be the time since the ball passed through photogate A (t AB ). x 0 be the position of the ball at time t = 0 (at photogate A). v 0 be the speed of the ball at time t = 0 (speed at photogate A). v be the speed at time t (speed at photogate B). x be the position of the ball at time t (position of photogate B). a be the acceleration of the rolling ball. b. Derive an equation for the acceleration of the ball in terms of the three times (t A, t B, t AB ) and the diameter of the ball (d B ). These are all quantities you can measure directly. C Doing the experiment Initial position (x 0, m) Position (x, m) Table 1: Experimental data Time Time through gate through gate A B (t A, sec) (t B, sec) Time from Ato B (t AB, sec) Speed at gate B (v B, m/sec) Answer Sheet 4.2 A Model for Accelerated Motion

28 D Preliminary analysis a. Use the data from Table 1 to make the speed versus time graph for the ball. Scale the graph so it starts from zero speed and zero time. The time axis (x) should be the time from photogate A to photogate B. The speed axis (y) should be the speed at photogate B. b. Use the data from Table 1 to make the position versus time graph for the ball. Scale the graph so it starts from zero position and zero time. The time axis (x) should be the time from photogate A to photogate B. The position axis (y) should be the position of photogate B. 4.2 A Model for Accelerated Motion Answer Sheet

29 c. The equation of a straight line is often given in the form y = mx + b. The variable m is the slope and the variable b is the y-intercept. The speed versus time graph should be a straight line; therefore, the equation should apply. Rewrite the equation for a straight line for the speed versus time graph using appropriate variables from the experiment (v, v 0, x, x 0, t AB, and so on). Make a table that shows how y, m, x, and b correspond to the real experimental variables. d. From your graph of speed versus time, estimate the initial speed and acceleration. Answer Sheet 4.2 A Model for Accelerated Motion

30 e. Use your formula derived in Part 2b to calculate the acceleration of the ball for a few different measurements. Compare your calculation with the value you estimated from the graph. E Testing the equations a. Calculate the position of the ball from the equations for uniformly accelerated motion. Use Table 2 for the results of your calculations. You need to use the initial speed, initial position, and acceleration you estimated from the speed versus time graph. Do the calculations for the same times (from A to B) as your measured data. b. Plot the calculation on the same graph as your measured data for position versus time. You can draw the calculation as a solid line on the graph since the equation predicts the entire curve. The experimental data should be left as unconnected dots. 4.2 A Model for Accelerated Motion Answer Sheet

31 c. How do your measured positions compare with the positions predicted by the equation? Table 2: Predicted and measured positions Time (sec) Predicted position (x, m) Measured position (x, m) d. Use the equation for uniform accelerated motion to calculate how long the track would have to be for the ball to reach a speed of 60 miles per hour. Answer Sheet 4.2 A Model for Accelerated Motion

32 Extra space for notes and performing calculations: 4.2 A Model for Accelerated Motion Answer Sheet

33 Name: 4.3 Free Fall and the Acceleration due to Gravity Question: How do you measure the acceleration of a falling object? A Setting up the experiment There are no questions to answer in Part 1. B A technique for dropping the ball from the right place There are no questions to answer in Part 2. C Determining g from experiment There are no questions to answer in Part 3. D Measuring data to determine g Table 1: Time and distance data h (m) Time, t A (sec) Time, t B (sec) Time, t AB (sec) E Analyzing the data Table 2: Calculation of g Iteration g (m/sec 2 ) v 0 (m/sec) Formula to use 1 equation 2 2 equation 3 equation 1 3 equation 3 equation 1 Answer Sheet 4.3 Free Fall and the Acceleration due to Gravity

34 a. Use the formula for distance traveled in free fall to derive equations 1, 2, and 3. b. Describe how the values for g change in successive iterations of the calculation. c. Make a graph showing each intermediate value of g on the y-axis and the iteration number on the x-axis. What does the graph show you about the calculation? 4.3 Free Fall and the Acceleration due to Gravity Answer Sheet

35 d. If you kept going with more iterations of the calculation would the value of g keep getting more and more accurate? Explain why or why not. e. Repeat the calculation for at least two more sets of data (trials). Calculate the average value for g for all three trials. Calculate the percent difference between your average value and the published value of 9.82 m/sec 2. How does your result compare to the accepted value? f. Which variable do you think has the largest uncertainty among the quantities you measured in the experiment? Why do you think so? Answer Sheet 4.3 Free Fall and the Acceleration due to Gravity

36 F Free fall and mass a. How does the value of g compare for the steel and plastic balls b. Explain any differences you find in part (a) if any. 4.3 Free Fall and the Acceleration due to Gravity Answer Sheet

37 Name: 5.1 The First Law: Force and Inertia Question: How does the first law apply to objects at rest and in motion? A Setting up the experiment There are no questions to answer in Part 1. B Reflecting on Newton s first law a. State Newton s first law in your own words. b. Place the steel ball in the center of the track so it stays at rest. What do you know about the forces on the ball? Identify the forces acting on it. c. If an object is moving and there are no unbalanced forces acting on it, does its speed increase, decrease, or remain the same? Explain. d. Push the ball with your finger and let it roll along the track. Does it appear to speed up or slow down? If so, you may wish to adjust the level of the track so that the ball seems to roll with constant speed. Answer Sheet 5.1 The First Law: Force and Inertia

38 C Creating constant speed motion a. Release the ball from the hill at the free end of the track. Allow it to roll through both of the photogates. If there are no unbalanced forces acting on the ball, how should the time it takes to pass through photogate A (t A ) compare with the time it takes to pass through photogate B (t B )? Explain. b. Read t A and t B on your Timer. How do the two values compare? What does this tell you about the speed of the ball as it rolls along the track? Continue to adjust the track until t A and t B are seconds apart or less. This takes repeated trials, so do not get discouraged. D Collecting data on the first law Positio n (cm) Table 1: Time and speed data Photogate A Photogate B Time Time t A (sec) Speed (cm/sec) Position (cm) Time t B (sec) Speed (cm/sec) t AB (sec) Accel. (cm/sec 2 ) E Analyzing the data a. Were any forces acting on the ball as it rolled along the level track? Identify the forces. Explain how Newton s first law is applied to describe the motion you observed. b. What changes occur in the forces acting on the ball when the track is tilted slightly up or down? Explain how the first law is applied to describe the observed motion in the case of uphill or downhill slope. 5.1 The First Law: Force and Inertia Answer Sheet

39 Name: 5.2 The Second Law: Force, Mass, and Acceleration Question: What is the relationship between force, mass, and acceleration? A B C Setting up the experiment There are no questions to answer in Part 1. Analyzing the system to find the tension in the string There are no questions to answer in Part 2. Measure forces and masses Table 1: Force and mass data D Thinking about force No. of washers Mass (kg) Force (N) Mass #1 m 1 = F 1 = Mass #2 m 2 = F 2 = a. Which way do the masses move? Does m 1 rise or fall? Does m 2 rise or fall? b. The three forces acting are T, F 1, and F 2. Based on your answers to (4a) above, arrange these forces in order from smallest to largest. Explain what physical reasoning you used to arrange the forces. Answer Sheet 5.2 The Second Law: Force, Mass, and Acceleration

40 E Measuring the acceleration Table 2: Distance, time, and acceleration data Time (sec) Distance (m) Acceleration (m/sec 2 ) String tension (N) a. Does the strength of the tension force in the experiment agree with your prediction from Part 4? b. If the pulley created a friction force, would the tension force in the string be larger, smaller, or stay about the same? (This is tricky because you need to consider the sides of the string separately.) 5.2 The Second Law: Force, Mass, and Acceleration Answer Sheet

41 Name: 5.3 The Third Law: Action and Reaction A Question: Can you identify action-reaction forces? Identifying action-reaction pairs For each of the situations described below, sketch the situation and identify at least one pair of forces that make up an action-reaction pair. a. A can of soda sitting on a table. b. A skateboarder pushing off the ground. c. A swimmer moving through the water. d. A runner pushing off from a starting block. Answer Sheet 5.3 The Third Law: Action and Reaction

42 e. A boater paddling through the water. B Identifying action-reaction pairs in your life a. List five specific activities you do on a weekly basis. For example, if you are on the tennis team, you might list hitting a tennis ball as one activity. b. Make a free body diagram of each activity. c. For each activity, identify at least one pair of forces that are an action-reaction pair. 5.3 The Third Law: Action and Reaction Answer Sheet

43 C Why don t equal and opposite forces cancel each other out? a. Create a sketch showing your calculator sitting on top of your textbook which is sitting on top of your desk which is standing on the tile floor. b. Identify the forces that serve as the action-reaction forces and draw them in your sketch. c. Now draw a free body diagram that shows each object by itself (the calculator, the textbook, the table, the tile floor, and Earth) and uses arrows to represent the forces acting on each particular object. d. Look at the forces on any one object. That object does not have both forces from any single actionreaction pair acting on it. Is this true for all of the objects? (This is the key to Newton s third law: The action-reaction forces are equal in size and opposite in direction but since they act on different objects, they do not cancel each other out.) Answer Sheet 5.3 The Third Law: Action and Reaction

44 D Thinking deeper about the third law Many important results in science are deduced by carefully thinking about what would happen if the opposite, or a different law, were true. For example, imagine if Newton s third law of motion was a law made by the government. Also, imagine there is going to be a vote tomorrow on whether to keep Newton s third law as it is or change the third law so every action force creates a reaction force that is always one-half as strong as the action force. Think up one strange scenario that might happen if forces obeyed a law in which the reaction force is opposite in direction and one-half as strong as the action force. You may wish to do this as a project jointly with your group. 5.3 The Third Law: Action and Reaction Answer Sheet

45 Name: 6.1 Mass, Weight and Gravity Question: What is the relationship between mass and weight? A B Setting up the experiment There are no questions to answer in Part 1. Analyzing the system to find the acceleration There are no questions to answer in Part 2. C A hypothesis that can be tested a. Rearrange the last equation to get a formula for the acceleration, a 1. b. Use the equations for uniformly accelerated motion to derive a formula that gives the time (t) it takes to fall a height (h) after the masses start moving. You may assume zero initial speed. The formula you get in (b) is actually a hypothesis that the experiment can test to see if the theory is correct. Note that we made some assumptions to arrive at this hypothesis. The assumptions are that there is no friction and that the pulley has no mass. 1. Measure the mass of each hanger (m 1 and m 2 ) and record the results in Table Calculate the predicted speed three seconds after release. D Measuring the speed There are no questions to answer in Part 4. Answer Sheet 6.1 Mass, Weight and Gravity

46 E Testing the hypothesis a. Discuss the accuracy and precision of the experiment. How much variability was there in the times you measured? What does that tell you about how well your experiment is able to test your hypothesis? b. Compare the predicted time with the measured time. Does your experiment confirm your hypothesis? How does your answer to question (a) above affect the conclusion of the experiment (whether the hypothesis is confirmed)? c. What factors might account for any difference between measurement and prediction? d. Can you think of a way to make the experiment a more sensitive test of your hypothesis by accounting for any of the factors you identified in part (c)? 6.1 Mass, Weight and Gravity Answer Sheet

47 Name: 6.2 Friction Question: How can we describe and model friction? A Static friction Table 1: Static friction data Mass (kg) Weight (N) Friction force (N) Ratio B Examining the data a. What happened to the friction force as the weight of the pulled objects increased? b. Discuss a possible explanation for the relationship. c. The ratio of the friction force to the weight of the pulled objects is called the coefficient of static friction. Was there a trend among these values or were they all roughly equal? d. What effect would placing the block on a rougher surface (such as sandpaper) have on the coefficient of static friction? Answer Sheet 6.2 Friction

48 . C Sliding friction Table 2: Sliding Friction Data Mass (kg) Weight (N) Friction force (N) Ratio D Comparing static and sliding friction a. What happened to the friction force as the weight of the pulled objects increased in Table 2? b. Is the relationship between the friction force and the total weight in Table 2 similar to the relationship in Table 1? c. The ratio of the sliding friction force to the total weight is called the coefficient of sliding friction. Compare the coefficient of sliding friction to that of static friction. Are they different? Is one significantly different than the other, or are the two coefficients about equal? d. Explain a possible reason the forces of static and sliding friction might not be equal. E Friction between other surfaces During the Investigation, you found the coefficients of static and sliding friction for felt on the tabletop. If time allows, determine the coefficients of friction for other combinations of surfaces. Some combinations you might try are the wood side of the block on a sheet of paper, felt on sandpaper, or wood on wood. 6.2 Friction Answer Sheet

49 Name: 6.3 Equilibrium of Forces and Hooke s Law Question: How do you predict the force on a spring? A Setting up the experiment Number of washers Table 1: Force and extension of a spring Attached mass (kg) Spring s position (cm) Calculated extension (cm) Calculated force (N) B Analyzing the data a. Make a graph of force versus extension for the spring. b. Use your graph of force versus extension to determine the spring constant for the spring in the experiment. Express your result in N/cm. Answer Sheet 6.3 Equilibrium of Forces and Hooke s Law

50 C Testing the model a. Use your graph to predict how much the spring should extend for a hanger with 20 washers. You need to determine the weight of 20 washers (and the hanger) to make your prediction. b. Set up the experiment and test whether the model (Hooke s law) gives the correct prediction. c. How close did your prediction come to the actual extension of the spring? Calculate the difference between the measurement and the prediction as a percentage of the actual measurement. D Compression springs Number of washers Table 2: Force and compression of a spring Added mass (kg) Spring s position (cm) Calculated compression (cm) Calculated force (N) 6.3 Equilibrium of Forces and Hooke s Law Answer Sheet

51 E Analyzing the data a. Make a graph of force versus compression for the spring. b. Use your graph of force versus compression to determine the spring constant for the spring in the experiment. Express your result in N/cm. F Testing the model a. Use your graph to predict how much the spring should compress when 20 washers are added. You need to determine the weight of 20 washers to make your prediction. Answer Sheet 6.3 Equilibrium of Forces and Hooke s Law

52 b. Set up the experiment and test whether the model (Hooke s law) gives the correct prediction. c. How close did your prediction come to the actual compression of the spring? Calculate the difference between the measurement and the prediction as a percentage of the actual measurement. d. Could this spring be used to measure the mass of one washer? If so, explain a procedure for how to make the measurement. If not, explain why not. e. How much force would it take to cause a compression of 1 millimeter? 6.3 Equilibrium of Forces and Hooke s Law Answer Sheet

53 Name: 7.1 Vectors and Direction Question: How do you give directions in physics? A Reading a compass There are no questions to answer in Part 1. B Making a map a. Take a sheet of graph paper and draw x- and y-axes pointing east-west (x) and north-south (y). b. Draw the first vector on the graph, which should be to scale. For example, if you had graph paper with a 1 cm grid, an appropriate scale would be to choose 1 cm = 1 meter. c. Draw the second vector starting from the end of the first vector. The graph paper now shows a map of two legs of a walking trip. d. Take the graph paper and draw a third vector from the end of the second vector back to the start this is the vector back home. Use a protractor and a ruler to measure the angle of the vector and determine its length in meters. Remember, you want compass bearings, so you should measure the angle clockwise from the positive y-axis, which is north on the compass. C Calibrating your pace Table 1: Step lengths Name Distance of 10 paces (m) Avg. length of 1 pace (m) D Walking the vectors Table 2: Vectors in units of steps Vector Distance in meters Distance in steps E Vectors in x-y coordinates a. Take a sheet of graph paper and draw x- and y-axes pointing east-west (x) and north-south (y). b. Draw the first vector on the graph. The graph should be to scale; 1 cm equals 1 meter might be a reasonable scale. For example, to draw the vector = (1,4)m, you would go over 1 cm in the positive x direction (east) and go up 4 cm in the positive y direction (north). c. Draw the second vector starting from the end of the first vector. The graph paper now shows a map of two legs of a walking trip. Answer Sheet 7.1 Vectors and Direction

54 d. Calculate the resultant vector by adding up the x and y components of the two vectors you already have. For example, if 1 = (1,4)m and 2 = (2,-6)m, then = (3,-2)m. e. The resultant vector is the vector you could have walked straight from the origin (home) to the final destination. To get back home, you need to walk the resultant vector in the opposite direction. Mathematically, that means multiplying the components by -1. In the example, the vector back home would be 3 = (-3,2)m. You can see on the map that this is correct. F Converting to compass coordinates Vector in x-y coordinates Table 3: Converting to polar coordinates Angle from north (degrees) Distance (m) Distance (steps) G Walking the vectors 1. There are no questions to answer in Part Vectors and Direction Answer Sheet

55 Name: 7.2 Projectile Motion and the Velocity Vector Question: Can you predict the landing spot of a projectile? A B Setting up the experiment There are no questions to answer in Part 1. Measuring the initial speed Table 1: Ball s time and speed Time (sec) Launch speed (m/sec) C Predicting the landing spot a. Work with your group members to come up with a theory that predicts the horizontal distance the ball moves before hitting the floor, The theory should take the form of a formula that involves only the initial height (y o ), initial speed (v o ), and the acceleration due to gravity (g). You should assume the ball leaves the track with a horizontal initial velocity. b. Using the average of the initial speeds you measured in Part 2, use the theory to calculate how far from the table the ball should land. D Testing the theory There are no questions to answer in Part 4. Answer Sheet 7.2 Projectile Motion and the Velocity Vector

56 E Analyzing the results a. How many centimeters is the landing spot from the center of the target? Did the ball travel too far, not far enough, to the left, or to the right? b. Measure and record the distance along the floor between the landing spot and the place where the ball left the track. If your measurements and calculations were accurate, this distance should be the same as the distance you calculated. c. Calculate the percent difference between the predicted distance and the actual distance the ball traveled. d. Discuss some sources of error in the Investigation that may have resulted in your ball not landing in the center of the target. e. When the ball was in the air, did its horizontal velocity change? Why or why not? f. When the ball was in the air, did its vertical velocity change? Why or why not? g. Calculate the velocity vector for the ball the moment before it hit the floor. Is the vector you calculate consistent with the motion of the ball after it hits the floor where the vertical component is abruptly reduced to zero? 7.2 Projectile Motion and the Velocity Vector Answer Sheet

57 h. Sketch each of the following graphs to describe the ball s motion as it was in the air: horizontal distance versus time, vertical distance versus time, horizontal speed versus time, and vertical speed versus time. Answer Sheet 7.2 Projectile Motion and the Velocity Vector

58 i. Imagine that you were to release the ball from a higher location on the track. Would you have to position the target closer to the table, farther from the table, or at the same distance? Why? j. Now imagine that you were to release the ball with the track on a table that is twice as high off the ground. How far would you have to position the center of the target from the edge of the track? Show any calculations you perform to get your answer. 7.2 Projectile Motion and the Velocity Vector Answer Sheet

59 Name: 7.3 Forces in Two Dimensions Question: How do forces balance in two dimensions? A B Setting up the spring scales There are no questions to answer in Part 1. Finding the force needed for equilibrium C The conditions of equilibrium Table 1: Finding a force to balance two 5-N forces Force 3 Magnitude (N) a. Calculate the x and y components of forces 1, 2, and 3 and enter the values in the table. Use a negative sign to indicate a direction in the negative x or y direction. b. Calculate the x and y components of the net force on the ring. Then use the Pythagorean theorem to calculate the magnitude of the net force on the ring. c. What should you have found the net force on the ring to be? Why? d. Why might the net force be slightly different from the theoretical value? Discuss some sources of error that may be causing inaccuracy in your results. Table 2: Finding a force to balance two 5-N forces Magnitude (N) x-component (N) y-component (N) Force 1 Force 2 Force 3 Net force Answer Sheet 7.3 Forces in Two Dimensions

60 D Determining the directions for equilibrium a. Use a protractor to determine the angles of the forces. Calculate the x and y components of the forces and record them in Table 3. Also, calculate the net force. Are the results what you expected? Your answer should say what your expectation was and why. Table 3: Finding two forces to balance one 5-N force Magnitude (N) x-component (N) y-component (N) Force Force 2 10 Force 3 12 Net force 7.3 Forces in Two Dimensions Answer Sheet

61 Name: 8.1 Motion in Circles Question: How do you describe circular motion? A Setting up an observation Circumference of the ball (step 2): Radius of the ball (step 3): Record your observations from step 6: B C Setting up an experiment There are no questions to answer in Part 2. Measuring the average linear speed Distance (cm) Time 1 (sec) Time 2 (sec) Table 1: Linear speed data Time 3 (sec) Avg. time (sec) Avg. linear speed (cm/sec) D Testing a hypothesis a. Remove the pulley and wrap a single turn of string around it. Use a meter stick to measure the diameter of the circle the string makes. Divide the diameter by two to get the radius of the pulley. This is the radius at which the string moves. b. Use the relationship v = ω r to calculate the average angular speed (ω) of the pulley in rad/sec. Answer Sheet 8.1 Motion in Circles

62 c. With linear speed, the distance (d) an object moves is calculated using the relationship d = vt where v is the linear speed and t is the time. Write a similar relationship between the angle (θ) an object rotates, its angular speed (ω), and the time, t. d. Use the relationship you just wrote in part (c) to calculate the total angle the pulley turns through while the falling mass moves from top to bottom. Express your answer in radians. There are 2π (about 6.28) radians in a full turn. An angle greater than 6.28 radians means the pulley rotated more than one turn. e. There are 10 stripes on the pulley for every radian of angle. You can measure the angle (in radians) the pulley turns by counting the stripes and dividing by 10. The Timer has a count mode that works perfectly for this purpose. Set the Timer in count mode. Move the masses from top to bottom by hand and record the number of stripes that pass the light beam. Calculate the total angle the pulley turns (in radians) by dividing the count by 10. NOTE: Pressing reset once clears the display, twice freezes the display, three clears it again, etc. If nothing seems to be counting, press reset again ONCE. How close did your predicted angle come to the angle you measured? 8.1 Motion in Circles Answer Sheet

63 Name: 8.2 Centripetal Force A Question: Why does a roller-coaster stay on track upside down on a loop? Introduction a. What do you observe as you dropped the ball from different heights? Think about the speed of the ball and whether it makes it around the loop successfully. b. Write down a hypothesis about the conditions that are necessary for a ball to make it successfully around the loop. B Thinking about centripetal force a. Using the formulas for weight and centripetal force, write a formula expressing the minimum speed (v) needed to keep the ball on the track. b. Use the formula to calculate the minimum speed required for the ball to make it around the loop and stay on the track. The radius of the track is 10 centimeters. c. Draw a free body diagram for the ball when it is at the top of the loop. Label the two forces acting on the ball and use vectors to show their directions. Answer Sheet 8.2 Centripetal Force

64 d. Explain why it would not be correct to draw a third arrow on your free body diagram and label it centripetal force. C Testing your theory Table 1: Experimental loop-the-loop data Mass (kg) Weight (N) Photogate time (sec) Speed (m/sec) Centripetal force at 10 cm radius (N) Did the ball stay on the track (yes or no) D Analyzing the results a. Compare the weight to the centripetal force for your experimental data on both balls. How should they be related? Do your experimental results confirm this? b. If a group in your class found the centripetal force to be significantly larger than the ball s weight in trial 1 for one of the balls, what would you suspect they did wrong? 8.2 Centripetal Force Answer Sheet

65 c. Describe how you would use the centripetal force and the weight to calculate the normal force on the ball. d. Imagine that your job is to design a roller-coaster layout containing a hill followed by a circular loop with a radius of 20 meters. Use what you learned in this Investigation to estimate the minimum speed required for the roller-coaster to make it around the loop. Do you have to take the mass of the passengers riding the roller-coaster into account in the previous question? Why or why not? e. Real roller-coasters are always designed to enter a loop after going down a hill that has more than the minimum height. Explain why. f. You may have noticed that many roller-coaster loops are not circular but teardrop-shaped. This is called a clothoid loop, and it has a smaller radius at the top than at the bottom. Use what you have learned in this Investigation to explain the advantages of a clothoid loop over a circular loop. Answer Sheet 8.2 Centripetal Force

66 Extra space for notes and performing calculations: 8.2 Centripetal Force Answer Sheet

67 Name: 8.3 Universal Gravitation and Orbital Motion A Question: How strong is gravity in other places in the universe? The gravitational force between everyday objects Use Newton s law of universal gravitation to calculate the gravitational force of attraction between the following pairs of objects. For each situation, estimate the masses of the objects and the distances between them. a. Your pencil and your calculator, having been placed next to each other on your desk. b. Your left shoe and your right shoe as you stand comfortably. c. You and another person of similar mass at a distance of two meters. d. Two cars parked next to each other. B The gravitational force of attraction between people and planets There are no questions to answer in Part 2. C Calculate your weight on different planets Use the law of universal gravitation and the information in Table 1 to calculate your weight at several different locations in the universe. Remember, the r in the formula stands for the distance between the centers of the two objects being considered. a. At the surface of Earth. b. At a distance of 1,000 kilometers above the surface of Earth. Answer Sheet 8.3 Universal Gravitation and Orbital Motion

68 c. At the surface of Jupiter. d. At a distance of 5,000 kilometers above the surface of Saturn. e. At the surface of Venus. D The value of g a. Set the weight (m 1 g) equal to the gravitational force (Gm 1 m 2 r 2 ) and solve the equation to get a formula for g in the form g =.... b. Calculate the value of g at the surface of each of the nine planets (including Earth) using the formula you found in Part a. Table 1: Mass and radius of the planets Planet Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto Value of g 8.3 Universal Gravitation and Orbital Motion Answer Sheet

69 c. On the surface of which of the nine planets would you weigh the most? On the surface of which would you weigh the least? How do you know? d. What happens to the strength of gravity as you get farther from the surface of a planet? Sketch a graph that illustrates this relationship. e. Advanced Problem: A bowling ball has a mass of about 5 kilograms. Suppose you shrank the ball until it had a surface gravity equal to Earth s (g = 9.8 N/kg). What would the radius of the ball be? A single atom has a radius of about meters. How does the size of the shrunken bowling ball compare with an atom? As strange as it seems, neutron stars exceed this incredible density! Answer Sheet 8.3 Universal Gravitation and Orbital Motion

70 Extra space for notes and performing calculations: 8.3 Universal Gravitation and Orbital Motion Answer Sheet

71 Name: 9.1 Torque A Question: How does force create rotation? Setting up the experiment a. Measure and record the mass of the hanger and its calculated weight. b. The radius of the pulley is 5 centimeters. Calculate the torque created by the weight of the hanger and washers. Give your answer in units of N-m. B Equilibrium and torque a. Calculate the torque created by the nuts and washers you added to the threaded rod. To do the calculation, use the distance measured from the spindle to the approximate center of the washers. b. If you move the washers farther from the center, does the torque increase or decrease? For this question, consider only the magnitude of the torque and not the direction. Answer Sheet 9.1 Torque

72 C Torque when the force and distance are not perpendicular a. Draw a diagram showing the torques acting on the system by the hanger on the string and the mass on the spinner arm. Make your drawing as accurate as you can, especially the angle of the spinner arm relative to horizontal. b. Explain why the system is not in equilibrium when the spinner is horizontal but is in equilibrium when the spinner is at a certain angle. Your explanation should use the concept of lever arm and include a diagram showing the lever arm for both torques acting on the system. 9.1 Torque Answer Sheet

73 Name: 9.2 Center of Mass A Question: How do objects balance? Locating the center of mass a. Remove the shape from the pencil and try to balance the shape on the tip of one finger at its center of mass. Try to balance the shape at other locations by supporting it with one fingertip. Explain why the shape balances at the center of mass but not at other points. b. Gently toss the shape up into the air in such a way that it rotates while it moves up and then back down. Watch the circle at the shape s center of mass while it spins. What do you notice? B Balancing books Length of one book (cm) Table 1: Book overhang distances Number of books Overhang distance (cm) a. Explain the method you used to determine how to position the books. Use the term center of mass in your explanation. Answer Sheet 9.2 Center of Mass

74 b. Make a graph of overhang distance versus number of books. Plot the distance on the y-axis and the number of books on the x-axis. c. Explain the relationship between the number of books and the overhang distance. Is it linear? d. How many books had to be stacked to reach an overhang distance of one book length? e. How many books do you think it would take to reach an overhang distance of two book lengths? 9.2 Center of Mass Answer Sheet

75 C Your body s center of mass a. Stand with your back and heels against a wall. Slowly bend down and try to touch your toes. Explain what happens and why. b. Position a chair so that it is facing you. Stand with your toes 2 feet away from the front edge of the chair. Bend over at the waist, touch the sides of the chair, and bend your body up to a standing position. Now bend over in the same way but grab the sides of the chair this time. Try to bend upward while holding the chair. Explain what happens and why. c. Why might these activities be easier for some students than for others? Answer Sheet 9.2 Center of Mass

76 Extra space for notes and performing calculations: 9.2 Center of Mass Answer Sheet

77 Name: 9.3 Rotational Inertia A Question: Does mass resist rotation the way it resists acceleration? Setting up the experiment a. Does the rod rotate faster when the washers are close to the center, near the outside, or does the position of the washers not affect the rotation speed? You may want to time how long it takes to spin 10 turns for both configurations. B Angular acceleration a. Assume that the mass of the pulley itself and the white plastic rod is so small that it may be neglected compared with the mass of the steel washers. Assuming the washers act like a single mass at a distance r from the axis, calculate the moment of inertia. Your answer should come out in units of kg-m 2. C Measuring angular acceleration a. Calculate the average time and period for the three trials of each variation. Use the averages to calculate the angular speeds (from the period) then the angular accelerations (angular speed divided by falling time). The result should come out in units of rad/sec 2. b. Compare the angular acceleration you measured in the two cases. Note that the mass is exactly the same in both cases. The torque applied is also exactly the same. Explain why the angular acceleration is different. Your explanation should use the concept of moment of inertia. Answer Sheet 9.3 Rotational Inertia

78 Extra space for notes and performing calculations: 9.3 Rotational Inertia Answer Sheet

79 . Name: 10.1 Machines and Mechanical Advantage Question: How do simple machines work? A Setting up the experiment Table 1: Input and output forces Number of pulleys Input force (N) Output force (N) 1 a. Compare the input and output forces using a single pulley. Is one larger than the other, or are they the same strength? B The block and tackle machine C Table 2: Input and output forces Number of strings Input force (N) Output force (N) Mechanical advantage a. Use your data from Table 2 to calculate the mechanical advantage for each arrangement of the ropes and pulleys. Record your calculations in Table 3. Table 3: Mechanical advantage Number of pulleys Output force (N) Input force (N) Mechanical advantage Answer Sheet 10.1 Machines and Mechanical Advantage

80 b. What is the relationship between the mechanical advantage and the configuration of the block and tackle machine? c. Explain in a few sentences why the mechanical advantage of a block and tackle machine should be what you proposed in (b). (This is a difficult question. HINT: The force in a string is the same anywhere in the string.) d. Describe how friction affects the mechanical advantage of a machine like the block and tackle. Would friction increase the mechanical advantage, decrease it, or have no effect? D A mechanical advantage problem a. Which pulley (the one on the left or the right) moves? b. Which group could use the smaller force to move the opposing team? 10.1 Machines and Mechanical Advantage Answer Sheet

81 Name: 10.2 Work Question: What are the consequences of multiplying forces in a machine? A Doing the experiment Mechanical advantage Table 1: Force and distance data Output Output force (N) distance (m) Both are the same for each trial Input force (N) Input distance (m) B Analyzing your data a. As the mechanical advantage increases, what happens to the length of the string you have to pull to raise the hanger? b. You may have heard the saying Nothing is free. Explain why this is true of the ropes and pulleys. (HINT: What do you trade for using less input force to lift the lower pulley block?) c. Write down a rule that describes the relationship between mechanical advantage and the input and output distances for the block and tackle machine. Answer Sheet 10.2 Work

82 C D What is work? There are no questions to answer in Part 3. Calculating work Table 2: Output and input work Mechanical advantage Output work (joules) Input work (joules) a. For each mechanical advantage, how do output and input work compare? b. Is output work ever greater than input work? Can you explain this? c. Explain any differences between input and output work in your data. E The relationship between work and energy There are no questions to answer in Part Work Answer Sheet

83 Name: 10.3 Energy and Conservation of Energy A Question: How is motion on a track related to energy? The energy of the ball a. Write down equations for the potential and kinetic energy of the ball. (note, the ball rolls) b. Where is the kinetic energy largest? Where is it smallest? c. Where is the potential energy largest and smallest? B Measuring the speed of the ball Position (cm) 5 Height (m) Table 1: Height, time, speed and energy data Time through photogate (sec) Speed (cm/s) Potential Energy (J) Kinetic Energy (J) Total Energy (J) Answer Sheet 10.3 Energy and Conservation of Energy

84 C Graphing the data a. Use your measurements to make a graph showing the relationship between speed and height. Plot the position of the photogate on the track on the x-axis. Plot both the speed and the height on the y-axis. You should have two separate lines on your graph. Use two different colors or types of lines (dotted and solid) to connect each set of points Energy and Conservation of Energy Answer Sheet

85 b. Plot a similar graph showing the potential energy, kinetic energy, and total energy on the y-axis and the position on the x-axis. D Analyzing the data a. What can you tell from your first graph? Describe the relationship between the speed of the ball and the height. Where is the speed of the ball the greatest? Where is it the least? Does this agree with your hypothesis? b. Does the uphill or downhill direction of the ball affect its speed, or is height the only important factor? Answer Sheet 10.3 Energy and Conservation of Energy

86 c. What can you say about the energy graph? Where is the potential energy largest and smallest? Where is the kinetic energy largest and smallest? How are the potential and kinetic energy related to the total energy? E Conservation of energy a. Right before the ball is released at the top of the hill, which type of energy does it have? What is the total energy of the ball? b. What happens to the ball s kinetic energy as it moves down the hill? What happens to its potential energy? c. Use the law of conservation of energy to derive a formula that relates the speed of the ball to its height (h) and the initial height (h 0 ) from which it was released. d. According to the equation you derived in part (c) above, what is the effect of mass on the speed of the ball? Measure the speed of the steel and plastic balls at the same position to test this hypothesis Energy and Conservation of Energy Answer Sheet

87 Name: 11.1 Efficiency Question: How efficient is the straight track? A B Setting up the straight track There are no questions to answer in Part 1. Collecting data Table 1: Time, height, and mass data for plastic ball Trial Time through photogate (sec) Initial height (m) Final height (m) Mass of ball (kg) Average Table 2: Time, height, and mass data for steel ball Trial Time through photogate (sec) Initial height (m) Final height (m) Mass of ball (kg) Average Answer Sheet 11.1 Efficiency

88 C Potential and kinetic energy Table 3: Potential and kinetic energy Type of ball Location on track Speed (m/sec) Kinetic energy (J) Potential energy (J) Total energy (J) D plastic top Efficiency bottom steel top bottom a. Compare the total energy of each ball at the top of the track to its total energy at the bottom. Did each ball s total energy increase, decrease, or remain unchanged? b. Calculate the efficiency for each ball. c. Compare the two efficiencies. Why might they be slightly different? 11.1 Efficiency Answer Sheet

89 d. The law of conservation of energy states that energy cannot be created or destroyed. If the efficiencies were less than 100 percent, does this mean the law of conservation of energy is not true? Was energy lost? Where did the energy go? Write a short paragraph explaining your answer. (HINT: The motion of the ball includes rotation as well as linear motion.) e. CHALLENGE! If the efficiency for the steel ball were 100 percent, how fast would it be moving at the bottom of the track? Answer Sheet 11.1 Efficiency

90 Extra space for notes and performing calculations: 11.1 Efficiency Answer Sheet

91 Name: 11.2 Energy and Power Question: How powerful are you? A Lifting power Table 1: Lifting data Name Weight (N) Distance (m) Time (sec) Work (J) Power (W) 1.5 B Comparing the data a. Why is the object s weight used in the calculation of work done? b. How did the amount of work done by each person compare? Why? c. What determined the power of each person? Explain. d. A typical light bulb has a power of 75 watts. How does this compare to your power output while lifting the object? Answer Sheet 11.2 Energy and Power

92 e. Discuss two ways you could increase the amount of work you do in this activity. f. Discuss two ways you could increase your power output in this activity. C Stair-climbing work and power Table 2: Stair-climbing data Name Weight (N) Vertical distance (m) Time (sec) Avg. time (sec) Work (J) Power (W) D What did you learn? a. How did the work done by the different people compare? In the first part of the Investigation, every group member did the same amount of work. Why was this not the case with the stairs? 11.2 Energy and Power Answer Sheet

93 b. Which person had the greatest power? Which two factors determined each person s power? c. Calculate the average work done and the average power for all of the stair climbers. d. How do the average amounts of work and power for the stair climbing compare with your own work and power when lifting the object in the first part of the Investigation? e. The human body is able to do work because energy is absorbed when we eat food. In physics, we usually measure work and energy in joules but food energy is usually measured in Calories. One Calorie is equal to 4,186 joules. Select one of the people who climbed the stairs and calculate the work done in Calories. These Calories come from food that is burned by the person s body. You may be surprised by how small the number is. f. Imagine that two people having equal weights climb the same flight of stairs. One runs and the other walks. Do they do the same number of Calories of work (in the physics sense)? Do they have the same power output? Explain. Answer Sheet 11.2 Energy and Power

94 Extra space for notes and performing calculations: 11.2 Energy and Power Answer Sheet

95 Name: 11.3 Energy Flow in Systems Question: Where did the energy go? A An energy flow diagram There are no questions to answer in Part 1. B Drawing energy flow diagrams Draw an energy flow diagram for each scenario described below. Your diagram must have enough detail to show at least three forms that energy takes. A short description (a few words) should accompany each different form of energy on your diagram. You may make your diagram as complex as you wish by including more forms of energy. a. A car drives down a hill and then up and over the top of another hill. b. A seagull in flight swoops down and snatches a fish to eat out of the water. Answer Sheet 11.3 Energy Flow in Systems

96 c. A calculator operates from a solar cell. d. A camper uses a wood fire to heat up a pot of water for tea. The pot has a whistle that lets him know when the water boils. e. A bicyclist rides at night, switching on her bike s generator so that the headlight comes on. The harder she pedals, the brighter the headlight glows Energy Flow in Systems Answer Sheet

97 . Name: 12.1 Momentum Question: What are some useful properties of momentum? A B Conservation of momentum and energy There are no questions to answer in Part 1. Making a collision There are no questions to answer in Part 2. C Observing and analyzing the collision a. Describe the motion of the projectile ball before and after the collision. b. Describe the motion of the target ball before and after the collision. D E F The discovery of the nucleus of the atom There are no questions to answer in Part 4. An experiment in momentum conservation There are no questions to answer in Part 5. Collecting the data Table 1: Time and speed data Projectile before collision Projectile after collision Target after collision Time (t 0 ) Speed (v 0 ) Time (t p ) Speed (v p ) Time (t t ) Speed (v t ) Answer Sheet 12.1 Momentum

98 G Analyzing the data a. Calculate the speeds of the projectile and target balls before and after the collision. Enter the results in Table 1. b. Write down the law of momentum conservation for the two balls using the variables in the diagram. c. Solve the momentum conservation equation for the mass of the target ball. Your answer should be a formula of the form m t =??? where the right-hand side of the equation includes only the mass of the projectile ball and the speeds before and after the collision. d. Calculate the mass of the target ball from the formula you derived in Part c. Measure the actual mass of the target ball. How close did your estimate come? e. Give at least one reason the predicted mass and measured mass may be different and cause the deviation you observed Momentum Answer Sheet

99 Name: 12.2 Force is the Rate of Change of Momentum A Question: How are force and momentum related? Force, momentum, and the second law a. Which collision creates the greater change in momentum? Remember, you need to consider the sign of the velocity before and after the collision when you calculate the change in momentum. B Observing elastic and inelastic collisions There are no questions to answer in Part 2. C Reflecting on what you observed a. Compare the velocities of the rubber ball and the clay ball just before they collided with the wood block. Are the velocities different or are they the same? b. Compare the momentum of the rubber ball and the clay ball just before they collided with the block. Does the rubber ball have more, less, or about the same momentum as the clay ball? c. Did the clay ball knock over the block? Explain the observations using the fact that force is equal to be rate of change of momentum. Which ball experienced a greater change in momentum during the collision with the wood block? Answer Sheet 12.2 Force is the Rate of Change of Momentum

100 Extra space for notes and performing calculations: 12.2 Force is the Rate of Change of Momentum Answer Sheet

101 Name: 12.3 Angular Momentum A Question: How does the first law apply to rotational motion? Thinking about angular momentum a. List three variables that determine the angular momentum of the rotating mass on a string. b. Discuss with your group what would happen if the radius of the circle were suddenly made smaller. Assume that the mass stays constant. How can the angular momentum stay the same when the radius decreases? Write a hypothesis describing what you believe will happen in an experiment where you are observing a mass revolving at the end of a string and the string is shortened during the motion. B C Setting up the experiment There are no questions to answer in Part 2. Observing the conservation of angular momentum There are no questions to answer in Part 3. D Reflecting on what you observed a. Explain how the conservation of angular momentum and the concept of moment of inertia apply to explain your observations from Part 3. Answer Sheet 12.3 Angular Momentum

102 b. In many diving competitions, the diver jumps from the board or platform, turns one or two complete somersaults, and straightens out to land in the water with arms and head straight down and feet straight up in the air. While completing the somersault, the diver s body is tucked in tightly. Before entering the water, the diver s body extends to straighten out. Use the conservation of angular momentum to explain how a diver can spin rapidly in a somersault and then reduce rotational speed to enter the water vertically. c. Angular momentum behaves like a vector. Unlike the linear momentum vector however, the angular momentum vector does not point in the direction of an object s velocity. Instead, the angular momentum vector points along the axis of rotation. You can use your right hand to determine its direction. When the fingers of your right hand curl in the direction of rotation, your thumb points in the direction of the angular momentum vector. The law of conservation of angular momentum applies to the direction of the angular momentum vector as well as its magnitude. It takes torque to change the direction of the angular momentum vector. The inverse is also true. If the direction of the angular momentum vector changes, reaction torques act back on the rotating object to resist the change. For example, it is harder to balance a bicycle that is standing still than a bicycle that is rolling. Use the conservation of angular momentum to explain why this is true Angular Momentum Answer Sheet

103 Name: 13.1 Harmonic Motion Question: How do we describe the back-and-forth motion of a pendulum? A B C The pendulum There are no questions to answer in Part 1. Setting up the pendulum There are no questions to answer in Part 2. The three pendulum variables I Mass (g) Amplitude (degrees) Table 1: Period, amplitude, mass, and length data String length (cm) Time from Timer (seconds) Period of pendulum (seconds) D Analyzing the data a. Of the three things you can change (length, mass, and angle), which one has the biggest effect on the pendulum, and why? In your answer, you should consider how gravity accelerates objects of different mass. Answer Sheet 13.1 Harmonic Motion

104 b. Split up your data so that you can look at the effect of each variable by making a separate graph showing how each one affects the period. To make comparison easier, make sure all the graphs have the same scale on the y-axis (period). The graphs should be labeled as shown in the example below: 13.1 Harmonic Motion Answer Sheet

105 Answer Sheet 13.1 Harmonic Motion

106 E Applying what you know a. Using your data, design and construct a pendulum that you can use to accurately measure a time interval of 30 seconds. Test your pendulum clock against the Timer set to stopwatch mode. b. Mark on your graph the period you chose for your pendulum. c. How many cycles did your pendulum complete in 30 seconds? d. If mass does not affect the period, why is it important that the pendulum in a clock be heavy? e. Calculate the percent error in your prediction of time from your pendulum clock. F Phase a. What is the relationship between the lengths of the strings if one pendulum has twice the period of the other? b. Describe how the phase of the pendulums in step 3 changes over time Harmonic Motion Answer Sheet

107 Name: 13.2 Why Things Oscillate A Question: What kinds of systems oscillate? Stable and unstable systems a. Describe your example of a stable system in one or two sentences. What happens when you push it a little away from equilibrium? Write one sentence that describes the motion. b. Describe your example of an unstable system in one or two sentences. What happens when you push the unstable system a little away from equilibrium? Write one sentence that describes the motion. B Restoring forces There are no questions to answer in Part 2. Answer Sheet 13.2 Why Things Oscillate

108 C Building an oscillator a. Create a system that oscillates. You may use anything you can find including springs, rubber bands, rulers, balloons, blocks of wood, or anything else that can be safely assembled. b. Draw a sketch of your system and identify what makes the restoring force. c. On your sketch, also identify where the mass that provides the inertia is located. D The natural frequency There are no questions to answer in Part 4. E Changing the natural frequency a. Describe and test a way to increase the natural frequency of your oscillator. Increasing the natural frequency makes the oscillator go faster. b. Describe and test a way to decrease the natural frequency of your oscillator. Decreasing the natural frequency makes the oscillator go slower Why Things Oscillate Answer Sheet

109 Name: 13.3 Resonance and Energy Question: What is resonance and why is it important? A B What is resonance? There are no questions to answer in Part 1. Creating resonance in a system There are no questions to answer in Part 2. C Reflecting on what you observed a. Explain how the force applied by the wiggler causes the response of the pendulum. Your answer should make direct reference to your observations and explain why the natural frequency is important. b. Make a rough sketch of a graph showing amplitude versus period. Your x-axis (period) should range from zero to at least twice the natural period. The graph is NOT a straight line or simple curve. Answer Sheet 13.3 Resonance and Energy

110 D Energy and harmonic motion a. If the frequency of an oscillator is increased, what happens to the total energy? Your answer should state whether you think the total energy goes up, goes down, or stays the same. Explain the physical reasoning behind your answer. b. If the amplitude of an oscillator is increased, what happens to the total energy? Your answer should state whether you think the total energy goes up, goes down, or stays the same. Explain the physical reasoning behind your answer. E Resonance and energy There are no questions to answer in Part Resonance and Energy Answer Sheet

111 . Name: 14.1 Waves and Wave Pulses Question: What is the speed of a wave? A The speed of a wave pulse There are no questions to answer in Part 1. B Reflecting on what you observed a. Describe how the speed of a wave differs from the speed of a moving object such as a car. HINT: What is it that moves in the case of a wave? b. How did the tension affect the speed of the wave pulse? C Measuring the speed of a wave Table 1: Initial data on the speed of the wave pulse Trial # Distance between photogates (m) Time from A to B (seconds) Speed of pulse (m/sec) Answer Sheet 14.1 Waves and Wave Pulses

112 D Changing the string tension String tension (N) Table 2: String tension data Distance between photogates (m) Time from A to B (seconds) Speed of pulse (m/sec) a. What effect does changing the tension have on the speed of the wave pulses? b. From what you know about forces, explain why you think the higher tension makes the waves move faster Waves and Wave Pulses Answer Sheet

113 Name: 14.2 Motion and Interaction of Waves A Question: How do waves move and interact with things? Making plane waves in a ripple tank a. Draw a sketch that shows the wave front of your plane wave. Also on your sketch, draw an arrow that shows the direction the wave moves. b. Is the wave front parallel or perpendicular to the direction the wave moves? c. Would you consider your water wave a transverse wave or a longitudinal wave? Answer Sheet 14.2 Motion and Interaction of Waves

114 B Circular waves a. Draw another sketch that shows the circular wave fronts and include at least four arrows that show the direction in which each part of the wave moves. b. At every point along the wave, are the wave fronts more parallel or perpendicular to the direction in which the wave moves? C Diffraction a. Sketch the shape of the wave fronts before and after the opening. b. Does the wave change shape when it passes through the opening? If you see any change, your answer should say what kind of shape the wave changes into Motion and Interaction of Waves Answer Sheet

115 D Reflection a. Draw a sketch that shows what happens to the wave front when it hits the side of the tray. b. Draw an arrow showing the direction of the wave approaching the side. c. Draw another arrow showing the direction of the wave after it reflects from the side. d. Do you see any relationship between the incoming and outgoing arrows? E Applying your knowledge a. You can easily hear a person talking through a crack in the door although you cannot see them. Do any of your observations provide a clue to how sound can get through tiny cracks? b. Ocean waves can get many meters high. Big waves on the ocean tend to occur on very windy days. Explain how wind might contribute to making big waves. Use a sketch in your explanation. Answer Sheet 14.2 Motion and Interaction of Waves

116 Extra space for notes and performing calculations: 14.2 Motion and Interaction of Waves Answer Sheet

117 Name: 14.3 Natural Frequency and Resonance Question: How do we make and control waves? A B Setting up the experiment There are no questions to answer in Part 1. Waves on the vibrating string C Table 1: Frequency, harmonic, and wavelength data Harmonic # Frequency (Hz) Wavelength (m) Frequency times wavelength Analyzing the data a. In one or two sentences, describe how the frequencies of the different harmonic patterns are related to each other. Answer Sheet 14.3 Natural Frequency and Resonance

118 b. Why is the word fundamental chosen as another name for the first harmonic? c. Give an equation relating frequency (f) and wavelength (λ) that best describes your observations. d. If the frequency increases by a factor of two, what happens to the wavelength? e. Propose a meaning for the number you get by multiplying frequency and wavelength. D Frequency and energy Table 2: Frequency vs. amplitude data Harmonic # Frequency (Hz) Amplitude (cm) 14.3 Natural Frequency and Resonance Answer Sheet

119 E Interpreting the data a. Make a graph showing how the amplitude changes with frequency. b. What happens to the amplitude of the waves as their frequency increases? Answer Sheet 14.3 Natural Frequency and Resonance

120 c. How does the energy of a wave depend on its frequency? For a given frequency, the amplitude of a wave depends on energy. More energy means larger amplitude. Assume the wiggler supplies the same amount of energy to each wave, independent of frequency. Use your observations of amplitude and frequency to propose a relationship between frequency and energy. d. Suppose you had two waves of different frequencies but the same amplitude. Which has more energy, the lower-frequency wave or the higher-frequency one? 14.3 Natural Frequency and Resonance Answer Sheet

121 Name: 15.1 Properties of Sound Question: What is sound and how do we hear it? A How high can you hear? B Table 1: How we hear frequencies of sound Description Frequency (Hz) Low Medium High Very high Testing the upper frequency limit of the ear a. The objective of the test is to determine how high a frequency people can hear. b. Make a histogram showing your class response to frequencies between 10,000 and 20,000 Hz. You should have 10 bars, one per 1,000 Hz. Each student who raises a hand is counted as a positive response on the graph. c. Do you think the method of counting raised hands is likely to give an accurate result? Give at least one reason you believe the method is either good or bad. Answer Sheet 15.1 Properties of Sound

122 . C Doing a more careful experiment Table 2: Frequency survey data # Right 10,000 Hz 12,000 Hz 14,000 Hz 16,000 Hz 18,000 Hz 20,000 Hz Plot another histogram showing only people whose choices matched the key all five times at each frequency. It is hard to fake a response (or guess) because you have to choose correctly five times for each frequency. This kind of experiment is called a double-blind test since neither you nor the researcher can see anyone else s response. The results from a double-blind experiment are much more reliable than other forms of surveys. Researchers use the double-blind method to test new medicines. D Probability, chance, and experiments a. What is the chance of guessing correctly every time with five trials? b. If 100 people did a true-false test with five trials and everybody guessed, how many people would be likely to make five correct choices in a row? 15.1 Properties of Sound Answer Sheet

123 c. Suppose there were three choices for each question. What is the chance of randomly guessing the right answer for a single question with three choices? d. You design an experiment to compare three sets of stereo speakers (A, B, and C). The same song plays sequentially on each set of speakers and people pick whether the first, second, or third sounded best. You set up a screen so your listeners cannot see the speakers. To rule out chance, you scramble the order in which you play each speaker and repeat the test three times. You figure if a person picks the same speaker all three times, it really must sound better than the other two. What is the chance that someone could randomly select the same set of speakers three times in a row? E Perceiving differences in frequency Make a data table like Table 3 that is large enough to hold all your results. Table 3: Comparative frequency data Frequency B Frequency Percent (Hz) diff. (Hz) diff. 1, % 1 1,000 1, % 15 1,000 1, % 0 Frequency A (Hz) a. Calculate the percent difference in frequency for each test. # of correct responses Answer Sheet 15.1 Properties of Sound

124 b. There are two ways to look at sensitivity. In one way, the ear responds to absolute differences in frequency. If the ear was sensitive to absolute differences, you would hear a 5 Hz difference no matter if the two frequencies were 500 and 505 Hz, or 5,000 and 5,005 Hz. The second possibility is that the ear only hears proportional differences. For example, suppose you could hear a proportional difference of 1%. That means you could tell the difference between 500 Hz and 505 Hz because the difference of 5 Hz is 1%. However, you could not hear the difference between 5,000 and 5,005 Hz because 5 Hz out of 5,000 Hz is a proportional difference of only 0.1 percent. To hear a 1% difference from 5,000 Hz, the second frequency would have to be 50 Hz higher or lower. Which model does the data support? 15.1 Properties of Sound Answer Sheet

125 Name: 15.2 Sound Waves Question: Does sound behave like other waves? A Beats There are no questions to answer in Part 1. B Interference a. Try to make an approximate measure of the wavelength of sound by changing the separation of the two speakers. The speakers have been moved one wavelength when the sound heard by the observer has gone from loudest, to softest, and back to loudest again. For this to work you need to keep the observer and both speakers in the same line. b. Interference can be bad news for concert halls. People do not want their sound to be canceled out after they have bought tickets to a concert! Why do we usually not hear interference from stereos even though they have two speakers? C Resonance Table 1: Resonant frequencies for tuning forks Tuning fork description Measured resonant frequency (Hz) Labeled resonant frequency (if any) Answer Sheet 15.2 Sound Waves

126 D Thinking about what you observed a. Did you observe any relationship between the size (or shape) of the tuning fork and the frequency at which it was resonant? b. What range of frequencies did you hear that seemed to match the frequency of the tuning fork? Give your answer in the form of a range written, for example, like 429 Hz Hz. c. Strike the tuning fork and hold the bottom end against a hard, thin surface such as a window. Does the sound get louder, softer, or remain unchanged? Explain what you hear by describing what might be happening between the tuning fork and the surface it touched. E Resonance in other systems Table 2: Resonant frequencies of glasses of water Trial # Water height Frequency (Hz) 15.2 Sound Waves Answer Sheet

127 Name: 15.3 Sound, Perception, and Music A Question: How is musical sound different from other sound? Chords a. Describe the sound of the three frequencies 264 Hz, 330 Hz, 396 Hz, and 528 Hz when you hear them together. b. Describe the sound of the three frequencies 264 Hz, 311 Hz, 396 Hz, and 528 Hz when you hear them together. c. Contrast the two sounds. Does one sound more happy or sad compared with the other? Does one sound spookier than the other? Which combination reminds you more of spring, which of fall? B Consonance and dissonance a. Give three examples of frequency pairs that are dissonant. b. Give three examples of frequency pairs that are consonant. Answer Sheet 15.3 Sound, Perception, and Music

128 C The musical scale a. Find two notes that sound dissonant when played together. b. Find two notes that sound consonant when played together. c. Suppose you wish to design a musical chime to play the notes C, E, and G. If the chime that plays the note C is 1 meter long, how long should you make the chimes that play the notes E and G? D Octaves Calculate the missing frequencies for each of the notes below using the rules for the octave. E The interpretation of sound a. Describe the construction of the human ear. What are the three major components? What part converts the vibration of a sound wave into signals that are carried by the auditory nerve? 15.3 Sound, Perception, and Music Answer Sheet

129 b. Research how many different frequencies of sound the human brain and ear can respond to. As a comparison, the eye contains about 120 million photoreceptors that each see a dot of brightness. The brain assembles the individual signals (dots) into a picture. The ear works in a similar way. The brain assembles a sonic picture from the signals received on the auditory nerve. c. Describe how an electronic keyboard or synthesizer is able to sound like many different instruments at the touch of a button. d. Suppose a 1.2 meter long string vibrates at a frequency of 440 Hz. What length of string would vibrate one octave higher? What length would vibrate one octave lower? Assume the tension in the string is the constant. Answer Sheet 15.3 Sound, Perception, and Music

130 e. (Challenge question) The western musical scale has 8 notes: do-re-mi-fa-so-la-ti-do, where the 8th note is an octave above the first. A piano keyboard has 12 keys spanning an octave. Describe why there are five extra keys (the black keys) between one note and the same note one octave higher. Your answer should be a short paragraph. f. (Challenge question) What sounds good to your ear is largely due to the sounds you heard during your childhood years. Different cultures use different musical scales. Some scales emphasize dissonance, others emphasize consonance. Research the musical scale of a different culture and describe the relationships between the notes Sound, Perception, and Music Answer Sheet

131 Name: 16.1 Properties and Sources of Light A Question: What are some useful properties of light? Fooling the brain with light a. Draw a sketch that uses lines to show how the light from the arrow on the paper reaches your eyes by reflecting from the mirror. B Seeing reflection and refraction at the same time a. Draw a diagram showing the path of the light when you see the X. v Answer Sheet 16.1 Properties and Sources of Light

132 b. Draw a diagram showing the path of the light when you see the O. c. Is the image in the prism always reflected or refracted or can there be both reflection and refraction at the same time? C The speed of light a. Measure the distance from the arrow you drew on the optics table to your eyes. b. Calculate the time it takes light to travel this distance. c. Calculate how far light would travel in one second Properties and Sources of Light Answer Sheet

133 D The inverse square law and light from distant stars and galaxies a. Suppose a star like the sun were a distance of meters away. What is the intensity of the light from that star that reaches Earth? b. How much time did the light take to get from the star to Earth? As we look out into the universe, we are also seeing backward in time because the light from distant stars and galaxies has traveled many years before reaching human telescopes. Using this technique, we are able to see more than one billion years back in time. c. A typical 100-watt light bulb makes about 20 watts of light and 80 watts of heat. Calculate the intensity of light from the bulb by using the light power (20 W) and the intensity formula. Repeat the calculation for a distance of 1 meter, 100 meters, and 500 meters away. A human eye is a very sensitive light detector; you can still see a 100-watt bulb at a distance of 500 meters. Answer Sheet 16.1 Properties and Sources of Light

134 Extra space for notes and performing calculations: 16.1 Properties and Sources of Light Answer Sheet

135 Name: 16.2 Color and Vision Question: How do we see color? A Mixing primary colors of light There are no questions to answer in Part 1. B Explaining what you see Use Table 1 to record the answers to the following questions about your observations. a. What color do you see when you mix red and green light? b. What color do you see when you mix red and blue light? c. What color do you see when you mix blue and green light? d. What color is produced when all three colors of light are equally mixed? Table 1: Mixing primary colors of light LED color combination Color you see Red + Green Green + Blue Blue + Red Red + Green + Blue C Breaking apart light Safety Note: DO NOT LOOK DIRECTLY AT THE LASER BEAM. Table 2: Examining light sources Red LED Green LED Blue LED White LED Red laser spot Answer Sheet 16.2 Color and Vision

136 D Explaining what you see a. Describe the similarities and differences you observed in the spectra from the red, blue, and green LEDs. You may want to use colored pencils to sketch the colors in the spectrum. b. Describe what you saw looking at the white LED. Compare the spectrum from the white LED with the spectra from red, green, and blue. You may want to use colored pencils to sketch the colors in the spectrum. c. Describe the spectrum you saw looking through the diffraction grating glasses at the spot made by the red laser on the screen. How is the spectrum of the red laser different from the spectrum of the red LED? d. Based on your observations, explain how the colored filters transform the white light of the LEDs inside the lamps into red, green, and blue Color and Vision Answer Sheet

137 Name: 16.3 Photons and Atoms Question: How does light fit into the atomic theory of matter? A B How is light produced? There are no questions to answer in Part 1. Examine the effects of light on glow-in-the-dark material There are no questions to answer in Part 2. C Recording and analyzing your results In answering these questions, think in terms of light and energy. Explain what happens to the energy in each of these situations: a. What happened when the light was not allowed to strike the glow-in-the-dark material? Explain. b. What happened when your hand was allowed to rest on the glow-in-the-dark material? Explain. D E Examining the effect of different colors of light There are no questions to answer in Part 4. The quantum theory of light There are no questions to answer in Part 5. Answer Sheet 16.3 Photons and Atoms

138 F Thinking about what you learned a. Based on the observations you made in Part 4, what color light has the highest energy? What color light has the lowest energy? Your answer should state how your observations support your conclusion. b. Intuitively you might think the more intense the light is that you shine, the more brightly the phosphorus should glow. Explain how your observations support or refute this hypothesis. c. How does what you observed support the quantum theory of light and atoms? HINT: What would have happened if electrons were free to absorb any energy rather than just certain energies? 16.3 Photons and Atoms Answer Sheet

139 Name: 17.1 Reflection and Refraction Question: How do we describe the reflection and refraction of light? A The law of reflection Table 1: Angles of incidence and reflection Diagram #1 Diagram #2 Diagram #3 Diagram #4 Angle of incidence Angle of reflection a. Write down your own statement of the law of reflection, describing the relationship between the angle of incidence and the angle of reflection. B C D Refraction There are no questions to answer in Part 2. Tracing rays through the prism There are no questions to answer in Part 3. Finding the index of refraction Table 2: Angles of incidence and refraction Angle/incidence Angle/refraction Going from air to glass Going from glass to air a. Draw the normals to the two faces of the prism the beam passed through. When light goes from a lowindex (air) to a higher-index (glass) material, does it bend toward the normal or away from the normal? Answer Sheet 17.1 Reflection and Refraction

140 b. When light goes from a high-index (glass) to a low-index (air) material, does it bend toward the normal or away from the normal? c. Use the two normals and a protractor to determine the angles of incidence and refraction for both surfaces crossed by the light beam. Use Table 2 to record the angles. d. Apply Snell s law to the light ray entering the prism. The incident material is air (n = 1); the refracting material is glass (n = n g ). Calculate the sines of the angles of incidence and refraction. Use your calculation to determine the index of refraction of glass (n g ). e. Apply Snell s law to the light ray leaving the prism. Using the index of refraction for glass, predict what the angle of refraction should be when the laser beam goes from glass to air. f. Compare your predicted angle of refraction to the angle you measured. Comment on any differences between your prediction and your measurement. Do your observations support Snell s law? Your answer should be supported by your observations of the laser beam. E The critical angle of refraction There are no questions to answer in Part Reflection and Refraction Answer Sheet

141 Name: 17.2 Mirrors, Lenses and Images Question: How does a lens or mirror form an image? A B The image in a mirror There are no questions to answer in Part 1. Refracting light through a lens There are no questions to answer in Part 2. C Analyzing what you observed a. Describe the path of the laser beam as it travels along the axis and through the lens. Compare the paths of the incident and the refracted rays. b. Describe the path of the laser beam as it travels parallel to the axis and above or below the axis. Compare the paths of the incident and refracted rays. c. The two refracted rays that you traced in Part 1 crossed the axis. Mark the axis where these rays crossed. This is the focal point for your lens. Due to imperfections in the lens, these two rays may not meet in exactly one point. In this case, choose the mid-point between the two points as your focal point. d. Measure the distance between the focal point and the center of your lens. This distance is the focal length of your lens. e. Label the focal point and focal length on your ray diagram. D Finding the image formed by a lens There are no questions to answer in Part 4. Answer Sheet 17.2 Mirrors, Lenses and Images

142 E Characteristics of the image a. Is the image larger or smaller? Calculate the magnification by dividing the length of the image by the length of the original arrow. b. Is the image right side up or is it inverted? c. Is the image closer to the lens than the original arrow or is it farther away? F The image from a single lens a. Was the image created by a single lens smaller or larger than the object? b. Was the image right side up or was it inverted? G Finding the magnification of a lens Distance to paper (cm) Table 1: Magnification data for a single lens # of squares on the graph paper (unmagnified squares) # of squares in the lens (magnified squares) Magnification 17.2 Mirrors, Lenses and Images Answer Sheet

143 Name: 17.3 Optical Systems Question: How are the properties of images determined? A Projecting an image with a lens Object dist. (cm) Table 1: Image data for a single lens Image orientation Image dist. (cm) Image height (mm) Magnification B Analyzing what you observed a. Make a scale drawing showing the positions of the object, lens, and screen. Measure and mark the near and far focal point of the lens. Draw an arrow for an object at the correct object distance from the lens corresponding to one of your experiments. Draw the three principle rays from the tip of the arrow using the rules above. The place where the rays meet is where the image forms. b. Measure the image distance from your drawing and the height of the image. The height of the image is the length of the image arrow from the optical axis to the tip. Make a similar scale drawing for each of your experimental trials. c. Record the theoretical image distance for each drawing in Table 2. Calculate and record the magnification, too. The magnification is the height of the image arrow divided by the height of the object arrow. Object dist. (cm) Table 2: Ray tracing analysis for a single lens Image dist. Image Image height (cm) orientation (mm) Magnification Answer Sheet 17.3 Optical Systems

144 d. How do your ray-tracing predictions compare with your actual measured images? Write one or two sentences comparing measured and calculated data. C Chromatic aberration a. With a prism, you may have observed that red light and blue light are bent by different amounts. This is why prisms spread light into a rainbow. In a lens, the effect is called chromatic aberration and it affects the color in images formed by lenses. How does chromatic aberration explain the difference you saw in the image distances formed with red and blue light? D E The thin-lens formula There are no questions to answer in Part 4. The image from a single lens Object distance (cm) Table 3: Predicted and measured image distances Focal length (cm) Predicted image distance (cm) Measured image distance (cm) a. How close did your prediction of the image come to the actual image? Answer with a percentage. b. Use the thin-lens formula to calculate the image distances for the previous experiments you did in Part 1 of this Investigation (Table 1). Do the calculations agree with the measurements? 17.3 Optical Systems Answer Sheet

145 Name: 18.1 The Electromagnetic Spectrum Question: What is the electromagnetic spectrum? A Researching your electromagnetic wave Your teacher will assign your group one type of electromagnetic wave that you will research using the Internet or reading. You will construct a poster displaying the information you gather about your type of wave. You will also present what you have learned to your classmates. All of the posters made by the class will be displayed in the order of the waves that make up the electromagnetic spectrum. Your research should include the answers to the following questions. Do not limit yourself to these questions; include other interesting information as well. Record the sources you use for a bibliography. 1. What is the range of wavelengths for your type of wave? 2. What is the range of frequencies? 3. What is the source of the wave? 4. Who discovered this type of wave and when? 5. Are these waves easily blocked or can they pass through objects? 6. Do the waves have an effect on people? Are they harmful? 7. Discuss the uses for the waves. These may include inventions that we use in our everyday lives, medical uses, or ways scientists use the waves for research. You should spend the greatest amount of time on this part of your research. B Sharing your information Organize your information on a poster. You should include drawings where they are appropriate. Make a bibliography of your sources and put it on the back of your poster. Present what you learned to the other groups in your class. You should be able to discuss the uses for your type of wave. Listen to the presentations made by other groups. Which type of wave do you think is the most useful to us? Why? Answer Sheet 18.1 The Electromagnetic Spectrum

146 Extra space for notes and performing calculations: 18.1 The Electromagnetic Spectrum Answer Sheet

147 Name: 18.2 Interference, Diffraction, and Polarization Question: What are some ways light behaves like a wave? A How a diffraction grating works There are no questions to answer in Part 1. B Measuring the wavelength of laser light a. Use the value for the spacing of the grooves on the diffraction grating from your instructor for d. Use the grating formula ( λ =dw L) to calculate the wavelength of the laser light (λ). b. Does the value of wavelength of the laser fall within with the range of wavelengths that appear red to the human eye? C The spectrometer Table 1: Spectrometer observations Apparent color Observed range of wavelengths Appearance of lines D Polarization of a transverse spring wave There are no questions to answer in Part 4. Answer Sheet 18.2 Interference, Diffraction, and Polarization

148 E Describing and applying what you see a. Describe the motion of the spring using the terms horizontal polarization and vertical polarization. Your description can be in words, diagrams, or both. b. Suppose you try to sandwich your spring wave between two boards. What happens to the waves if you make them pass through the narrow space between the boards? If the boards were oriented like the picture below, discuss how the two different polarizations of waves would behave. Which would get through the slot and which would be blocked? c. Describe the polarization of water waves. Are there two polarizations (like the spring) or only one? What is it about a water surface that makes it different from a spring? F The polarization of light There are no questions to answer in Part Interference, Diffraction, and Polarization Answer Sheet

149 G How do you explain what you see? a. The light from the sun (or a lamp) is not polarized, meaning it is a mixture of light that is polarized equally in all directions. Explain why the light is reduced passing through one polarizer. b. When the light passes through the first polarizer, it becomes polarized. We say light is polarized when it consists of only one polarization. Explain why rotating the second polarizer changes the amount of light you see coming through. c. The glare from low-angle sunlight reflecting from water and roads is polarized in the horizontal direction. Ordinary sunlight is not polarized. Explain how polarizing sunglasses can stop most of the glare but still allow half the regular (unpolarized) light to come through. Answer Sheet 18.2 Interference, Diffraction, and Polarization

150 Extra space for notes and performing calculations: 18.2 Interference, Diffraction, and Polarization Answer Sheet

151 Name: 18.3 Special Relativity A Question: What are some of the implications of special relativity? When does special relativity become important? a. A high-performance aircraft flies at a speed of 1,340 m/sec, or 4 times faster than the speed of sound (340 m/sec). At this high speed, will the effects of time dilation be perceived by a person with an ordinary watch? b. A rocket traveling to Mars must have a speed greater than the minimum speed required to break Earth s gravitational attraction. This minimum speed is called the escape velocity. Use research to find Earth s escape velocity. Is the escape velocity fast enough that relativity must be considered for normal purposes such as synchronizing two clocks? c. The numbers in Table 1 were calculated using a formula proposed by Einstein. Research the formula to identify what the variables mean. Answer Sheet 18.3 Special Relativity

152 B Relativity and frames of reference a. There are two reference frames important to understand the motion of the darts. What are they and what are their relative velocities? b. What is the speed of the first dart relative to the train? c. What is the speed of the first dart relative to the ground? d. How fast does the second dart approach the dart board on the pole? C The equivalence of mass and energy a. Calculate the amount of energy used by a 100 W light bulb that is left on continuously for one year. b. Suppose you could extract all of the energy in 1 kg of mass with 100 percent efficiency. How long could this amount of energy keep the 100 W light bulb lit. Give your answer in years Special Relativity Answer Sheet

153 c. Nuclear reactors convert a tiny fraction of the mass of uranium atoms into energy. Assume that 0.07% of the mass of uranium is converted to energy. How much energy do you get from 1 kg of uranium in a nuclear reactor? d. To appreciate the energy obtained from a kg of uranium, estimate the electric power used by a city of one million people. Assume that each person in the city uses an amount of electricity equal to 10 light bulbs that use 100 watts each. Calculate the total energy used by multiplying the total power in watts by the number of seconds in one year (you will get a very large number). e. How many kilograms of uranium must be used in a nuclear reactor to produce this amount of energy? f. One barrel of ordinary gasoline yields about joules of energy. Calculate how many barrels of gasoline are required to produce the energy you estimated in Part d. Answer Sheet 18.3 Special Relativity

154 Extra space for notes and performing calculations: 18.3 Special Relativity Answer Sheet

155 Name: 19.1 Electric Circuits A Question: What is an electric circuit? Building circuits with a battery, a bulb, and a wire a. Using only one battery, one bulb, and one wire, find four different ways you can arrange these three parts to make the bulb light. As you work, determine the kinds of connections that are needed to make the circuit work. b. Record all your circuit attempts. Draw both successful and unsuccessful attempts.the drawing at right shows a simple way to draw the bulb, battery, and wire. c. Make sure your drawings show the difference between the two ends of the battery. Also show exactly where the bulb is touching the wire and the battery. d. Explain why you think some configurations work and others do not. Record your first thoughts and impressions and don t worry if they are right or wrong. B C Using the electric circuits set There are no questions to answer in Part 2. Drawing circuit diagrams There are no questions to answer in Part 3. Answer Sheet 19.1 Electric Circuits

156 D Observing how a switch works a. Examine the switch as it turns the bulb on and off. Explain how the switch works. You may use both words and drawings. E What did you learn? a. Water can travel through air but cannot travel through a solid. Using what you learned in this Investigation, describe some materials that electricity can and cannot travel through. b. The word circuit comes from the same root as the word circle. Describe the similarities between a circle and the circuits that you built. c. A circuit that is on and working is sometimes called a closed circuit. Based on your observations of the switch, explain what closed means in a circuit. d. A circuit that is off or that is not working is sometimes called an open circuit. Based on your observations of the switch, explain what open means in a circuit Electric Circuits Answer Sheet

157 Name: 19.2 Current and Voltage Question: How does current move through a circuit? A B Building test circuit #1 There are no questions to answer in Part 1. Measuring current through test circuit #1 Follow the procedures and record your readings below: C Test circuit #2 Follow the procedures and record your readings below: D What did you learn about current? a. Review the two current readings for circuit 1. What conclusions can you draw from these results? b. Review the three current readings for circuit 2. What conclusions can you draw from these results? c. Transfer all your results for circuit 1 and circuit 2 into the table below. Compare the current readings in the two circuits. What happened to current when you added a bulb to the circuit? Current in circuit 1 (amps) Point A.092 Point A.070 Point B.091 Point B.070 Point C.068 Current in circuit 2 (amps) Answer Sheet 19.2 Current and Voltage

158 d. In which circuit were the light bulbs brighter? Offer a possible explanation for this. E Measuring voltage across a battery Follow the procedures and record your readings below: F Measuring voltage across a battery and bulb in a circuit Follow the procedures and record your readings below: G What did you learn about voltage? a. Were your predictions correct? b. Was there much difference in the battery voltage when it was not lighting the bulb and when it was? c. How did the battery s voltage compare with the bulb s voltage? Why do you think this is? 19.2 Current and Voltage Answer Sheet

159 H Building circuits with two batteries a. Describe how you should wire batteries together to light the bulb. b. Each battery is 1.5 volts. Explain how to calculate voltage when two batteries are connected. c. Compare the brightness of a bulb in a one-battery circuit to that of a bulb in a two-battery circuit. How is the bulb s brightness related to energy transfer in each circuit? d. Explain the meaning of the voltage reading across the bulb. Answer Sheet 19.2 Current and Voltage

160 Extra space for notes and performing calculations: 19.2 Current and Voltage Answer Sheet

161 Name: 19.3 Electrical Resistance and Ohm s Law Question: How are voltage, current, and resistance related? A a Resistance and current Explain why the current changes when the dial of the potentiometer is turned. The dial controls the resistance of the potentiometer, which varies from 0Ω (ohms) to 105Ω. b. Explain why the bulb is dim or bright depending on the position of the potentiometer. Your answer should use the concepts of resistance, energy and current. B The current and voltage relationship for a fixed resistor Table 1: Voltage vs. current Potentiometer setting Current (A) Voltage (V) Answer Sheet 19.3 Electrical Resistance and Ohm s Law

162 C Finding the relationship between voltage, current, and resistance a. Examine the data in Table 1. Describe in words what happens to the voltage across the fixed resistor as the current decreases. b. Graph the data from Table 1. Put voltage on the y-axis and current on the x-axis. Label your x- and y- axes and title your graph. c. Draw a best-fit line that matches the trend of the points on your graph. Calculate the slope of the line. d. The resistance of the green fixed resistor is 5 ohms. How does this value compare with the slope of your graph? e. The equation that relates current, voltage, and resistance is called Ohm s law. Write the mathematical equation for Ohm s law using V for voltage, I for current, and R for resistance Electrical Resistance and Ohm s Law Answer Sheet

163 D Voltage and current for a light bulb Table 2: Voltage vs. current for a bulb Potentiometer setting Current (amps) Voltage (volts) E Analyzing the bulb s current, voltage, and resistance a. What happened to the brightness of the bulb as you deacreased the current? b. Graph the data from Table 2. Put voltage on the y-axis and current on the x-axis. Label your x- and y- axes and title your graph. Answer Sheet 19.3 Electrical Resistance and Ohm s Law

164 c. Compare the shape of the graph for the light bulb to the shape of the graph for the fixed resistor. d. Use Ohm s law to calculate the resistance of the light bulb for each pair of voltage and current values. e. How is the resistance of the light bulb related to the amount of current through it? f. Discuss a possible reason for the bulb s resistance changing Electrical Resistance and Ohm s Law Answer Sheet

165 Name: 20.1 Series and Parallel Circuits Question: How do series and parallel circuits work? A Voltage and current in series circuits Table 1: Comparing series circuits Battery voltage (V) Current (A) Bulb 1 voltage (V) Bulb 2 voltage (V) Bulb 3 voltage (V) 1-bulb circuit 2-bulb circuit 3-bulb circuit B Thinking about what you observed a. Use the data in Table 1 to explain the relationship between the battery voltage in a circuit and the voltage across the bulb or bulbs connected in series. b. What did you notice about the brightness of the bulbs as you increased number of bulbs in the circuit? Why do you think this is? How do the measurements you made support your hypothesis about why the bulbs changed in brightness? c. What happens to the other two bulbs when one bulb is removed from the three-bulb circuit? Explain why the circuit behaves as it does. Answer Sheet 20.1 Series and Parallel Circuits

166 C a Determining the total resistance of resistors in series You will use two 5-ohm and one 10-ohm resistor during this Investigation. Predict what the total resistance of the circuit will be when all three resistors are connected in series. b. Predict the circuit s total current when 3 volts are applied using two batteries. D Measuring the current and resistance in series circuits Table 2: Three-resistor series circuit measurements Current (amps) Voltage (V) Resistance (ohms) a Use Ohm s law (in the form R = V/I) to calculate the total resistance in each circuit from the combined battery voltage (Table 1) and the current for each circuit (Table 2). Record your results in the bottom row of Table 2. b. Compare your measurements with the predictions of Part 3. Explain the effect that adding resistors has on the current flowing in a series circuit. E Parallel circuits Table 3: Comparing series circuits Voltage (V) Current (A) Resistance (Ω) Total circuit Bulb 1 Bulb 2 Bulb Series and Parallel Circuits Answer Sheet

167 F Comparing series and parallel circuits a. Use Ohm s law and the total circuit voltage and total circuit current from Table 3 to calculate the total resistance of the circuit with three bulbs in parallel. Record the result in the last row of Table 3. b. Use Table 4 to summarize the total circuit current and voltage measurements from the single-bulb circuit and the two different three-bulb circuits (series and parallel). Table 4: Comparing series and parallel circuits Current (A) Voltage (V) Resistance (Ω) Single-bulb circuit 3-bulb series circuit 3-bulb parallel circuit c. Compare the total resistance of the single-bulb circuit with the total resistance of the three-bulb series circuit. Which circuit resistance is greater? Why do you think this is? d. Compare the total resistance of the single-bulb circuit to the total resistance of the three-bulb parallel circuit. Which circuit resistance is greater? Why do you think this is? e. How are the branch currents in the parallel circuit related to the total current supplied by the batteries? Explain how you arrived at your answer. f. Compare the total current in the single-bulb circuit, the three-bulb series circuit, and the three-bulb parallel circuit. Is there an approximate relationship between the currents that also agrees with the observed brightness of the bulbs in each circuit? Answer Sheet 20.1 Series and Parallel Circuits

168 g. If you wish to brightly light three bulbs with one battery, should you connect them in series or parallel? h. Calculate the total current that should flow when three resistors (of 5, 5, and 10 ohms) are connected in parallel as shown. Build and test the circuit to evaluate your prediction. How close was your prediction to the actual measurements? 20.1 Series and Parallel Circuits Answer Sheet

169 Name: 20.2 Analysis of Circuits Question: How do you analyze network circuits? A Determining the resistance of each resistor Table 1: Measured resistance values R1 R2 R3 R4 Resistance (Ω) B Building a network circuit Record the data in the table. C Analyzing the circuit Table 2: Voltage and current measurements Voltage (volts) Current (amps) Battery (total circuit) R1 R2 R3 a. Which of the two resistors is connected in parallel? b. Which resistor is in series with the other two? c. How does the voltage across the parallel resistors (R 2 and R 3 ) compare? d. How does the voltage across the parallel resistors relate to what you learned about voltages in a parallel circuit in the previous Investigation? e. Voltage is the measure of the amount of energy carried by the current in a circuit. Trace the path of the current from the positive end of the battery, through the circuit, to the negative end of the battery. There are two possible paths because of the parallel part of the circuit but each path will only pass through two of the resistors. Does the amount of energy lost through the resistors equal the amount of energy supplied by the battery? Is this the case for each possible path? Explain. Answer Sheet 20.2 Analysis of Circuits

170 f. How does the current flowing through R 1 compare with the current through R 2? g. How does the current coming out of the battery compare with the sum of the currents flowing through R 2 and R 3? Explain this relationship. h. Use what you know about series and parallel circuits to calculate the theoretical total resistance of the circuit. i. Now calculate the total resistance of the circuit using Ohm s law, the battery voltage, and the total circuit current you measured. j. How does the total resistance calculated using Ohm s law compare with the theoretical total resistance found above? D Predicting the effect of changing a resistor a. Replace the10-ohm resistor (R 3 ) with the 20-ohm resistor (R 4 ). Use what you have learned about network circuits to predict the total circuit resistance and total circuit current. Show the process you used to make your predictions. b. Measure the voltage across the battery and each resistor and the total current in the circuit. Use Ohm s law to find the total circuit resistance. You will need to make a data table similar to Table Analysis of Circuits Answer Sheet

171 c. How did the predicted values compare with the measured ones? E A circuit puzzle a. When bulb B is disconnected, does bulb A get dimmer, brighter, or stay the same? b. When bulb B is disconnected, does bulb C get dimmer, brighter, or stay the same? c. Use what you know about series and parallel circuits to propose an explanation for what you observed. F Challenge: Analyze a four-resistor network circuit a. Build the circuit shown in the diagram at right. b. Use what you have learned about network circuits to predict the total circuit resistance and current. Show the process you used to make your predictions. c. Use the meter to measure the voltage across the battery and each resistor and the total circuit current. Use Ohm s law to find the total circuit resistance. d. How did the predicted values compare with the measured ones? Answer Sheet 20.2 Analysis of Circuits

172 Extra space for notes and performing calculations: 20.2 Analysis of Circuits Answer Sheet

173 Name: 20.3 Electric Power, AC, and DC Electricity A Question: How much does electricity cost? Find the power rating of home appliances a. Fill out the first two columns of Table 1 as you find the power rating of each appliance. The second column should be in kilowatts. b. Convert any power ratings listed in watts to kilowatts. To convert to kilowatts, divide the number of watts by 1,000. For example, 1,500 watts is equal to 1,500 1,000, or 1.5 kilowatts. c. Estimate the number of hours the device is used each month. Assume that one month equals 30 days. If your coffee maker is used for a half hour each morning, you would calculate a monthly usage of 15 hours (0.5 hr/day 30 days). Table 1: Power rating, usage, and cost of household appliances Appliance Power rating in kw Est. usage hrs. per mo. No. kwh per mo. Price per kwh Total cost per mo. B Estimate the number of kilowatt-hours each appliance uses in a month a. Multiply the power rating in kilowatts (from the second column) by the number of hours the appliance is used each month. For example, if you use a 1-kilowatt toaster for five hours a month, multiply 1 times 5. Write your answers in column 4 of Table 1 as shown in the sample below: Appliance Power rating in kw Est. usage hrs. per mo. No. kwh per mo. Price per kwh Total cost per mo. Microwave 1.4 kw 22 hours 30.8 C D Determine the monthly cost of using your appliances a. Find out how much you pay per kilowatt-hour. In some areas, one utility company provides all the electricity to an entire region while in other places several companies compete for customers. b. Write the price per kilowatt-hour in column 5 of Table 1. c. Calculate the amount of money your household spends to operate each appliance during one month. Multiply the kilowatt-hours per month by the price per kilowatt-hour to determine your cost. Analyze your data a. Compare your results with those of the other members of your group. List the three appliances from your group that had the highest power ratings in Table 2. Answer Sheet 20.3 Electric Power, AC, and DC Electricity

174 b. Think about the function of each appliance listed in Table 2. What kind of work is being done? In other words, electrical energy is converted into what other type(s) of energy? c. Do you see any similarities in the kinds of work being done by the three appliances in Table 2? If so, what are these similarities? d. Suggest one practical way you or another group member could reduce your electricity bills. e. Discuss the effect of climate on electricity use. What climate factors might influence which month has the peak electricity use in your area? f. Name one other factor (not related to climate) that may influence which month has the highest electricity use in your area. Table 2: Appliances with the highest power ratings Appliance Power rating in kilowatts 20.3 Electric Power, AC, and DC Electricity Answer Sheet

175 E What do you buy from the electric utility company? a. Which units in the last equation cancel? b. After canceling the units that appear in both the numerator and denominator, what fundamental unit remains? c. Is the remaining unit a measure of energy, work, or power? d. Do electric companies sell energy, work, or power? Answer Sheet 20.3 Electric Power, AC, and DC Electricity

176 Extra space for notes and performing calculations: 20.3 Electric Power, AC, and DC Electricity Answer Sheet

177 Name: 21.1 Electric Charge Question: How do electric charges interact? A B C Building a simple electroscope There are no questions to answer in Part 1. Creating static charges: Part I There are no questions to answer in Part 2. Observing the interaction between the tapes: Part I Follow the procedures and record your observations below: D E Creating static charges: Part II There are no questions to answer in Part 4. Observing the interaction between the tapes: Part II Follow the procedures and record your readings below: F What did you learn? a. How many types of interactions did you observe between the pieces of tape? Answer Sheet 21.1 Electric Charge

178 b. The first tapes you prepared pushed each other away, or repelled, each other. These two pieces of tape have the same kind of charge. This makes sense since you prepared the tapes in the same way. On the other hand, the A tape has one kind of charge and the B tape has a different kind of charge. Are the first tapes you prepared both A tapes or both B tapes? Explain how you figured this out. c. Give your hypothesis for how the A and B tapes might have acquired different kinds of charge. G Extension: Using the electroscope to detect other charged objects In sixteenth-century England, William Gilbert, the queen s physician, built the first electroscope. He noticed that the electroscope attracted lightweight objects. See if you can reproduce his results. 1. Remove the tape from your electroscope. 2. Prepare and label a fresh set of A and B tapes and place them on two arms anchored in one piece of clay. 3. Take light objects such as thread, small pieces of paper, and hair and slowly bring them close to both the A and B tapes. 4. Record your observations Electric Charge Answer Sheet

179 B Charged balloons Table 1: Balloon charging data Name: 21.2 Coulomb s Law A Question: How strong are electrical forces? Electrical forces in a penny a. A single proton or electron has a charge of coulombs. How many coulombs of protons and electrons are in each penny? b. Imagine you have two pennies, A and B. You remove all of the electrons from penny A and place them on penny B. Is penny A positively or negatively charged? Is penny B positively or negatively charged? c. Calculate the force of attraction between the two pennies if they are held 1 meter apart. d. A diesel locomotive weighs approximately 1,000,000 newtons. Determine the number of locomotives necessary to have a weight equal to the strength of the force between the pennies. e. You were probably surprised when you calculated the force between the pennies. What does your answer tell you about the amounts of charge normally transferred in activities such as brushing your socks on carpet or rubbing a balloon on your hair? Mass of balloon A (kg) Trial Distance (m) 1 2 Answer Sheet 21.2 Coulomb s Law

180 C Analyzing the data a. How did the distance in trials 1 and 2 compare? Why do you think this is? b. When the interaction between the balloons causes the string to become slack (tension is zero), what two forces on balloon A must be equal? c. Calculate the weight of balloon A. d. Use Coulomb s law to calculate the charge on each balloon (in coulombs) for each trial. You can assume each balloon is charged the same amount. e. Calculate the number of excess electrons on the balloons in each trial Coulomb s Law Answer Sheet

181 Name: 21.3 Capacitors Question: How does a capacitor work? A Current and voltage for a capacitor There are no questions to answer in Part 1. B Setting up the experiment a. Describe the flow of current when switch 1 is closed and switch 2 is open. This is the charging circuit for the capacitor. b. Describe the flow of current when switch 2 is closed and switch 1 is open. This is the discharging circuit for the capacitor. C Charging and discharging the capacitor Enter your data into Tables 1 and 2 below. Answer Sheet 21.3 Capacitors