CALIFORNIA STATE UNIVERSITY, SAN BERNARDINO. Physics 100. Physics in the Modern World

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1 CALIFORNIA STATE UNIVERSITY, SAN BERNARDINO Physics 100 Physics in the Modern World John McGill Revised 2007: Diana Wall and Linh Phan Revised 2009: John McGill and James Sheu Revised 2012: Diana Wall - 1 -

2 Table of Contents 1. Units and Measurements 4 Principles: Units, Measuring, Volume, Density, Uncertainties, Significant Digits Equipment: Ruler, large beaker, graduated cylinder, scale, density set 2. Variables and the Pendulum 12 Principles: Variables, Graphing, the Pendulum, Hypothesis Testing Equipment: Meter stick, mass set, lab stand with protractor, string, stop watch 3. Free Fall 23 Principles: Motion: Speed and Acceleration, Gravity Equipment: Ruler, Computer, Science Workshop interface, Photogate, Picket fence 4. Levers 30 Principles: Levers, Work, Balance Equipment: Balance bar and stand, mass set 5. Conservation of Energy 37 Principles: Hooke s Law, Weight, Energy: Kinetic, Gravitational, Elastic and Conservation Equipment: Meter stick, mass set (new), lab stand & attachments, spring, photo gates and timer 6. Specific Heat 48 Principles: First, Second and Third Laws of Thermodynamics, Specific Heat Equipment: Thermometer, water heater, calorimeter, lead, copper, and aluminum objects - 2 -

3 7. Waves 54 Principles: Waves, Wavelengths, Frequency, Standing Waves, Resonance Equipment: Meter stick, mass set, mechanical wave driver, signal generator, string, pulley, lab stand with hook, wires 8. Electricity 62 Principles: Electricity, Electric Charge, Electromagnetic Fields, Electric Circuits, Current, Voltage, Alternating and Direct Currents, Ohm s Law, Resistance, Electric Power Equipment: Analog voltmeter and ammeter, hand held generator, battery pack, resistor, series resistors, parallel resistors, light bulb and base, wires 9. Electromagnetism 72 Principles: Electromagnets, Magnetic Fields, Induction, Transformers Equipment: 200, 400, and 800 turn coils, transformer core, signal generator, bar magnets, battery pack, compass, light bulb and base, galvanometer 10. Light Reflection and Refraction 82 Principles: Light, Reflection, Refraction, Snell s Law, Lenses, Mirrors, Optical Instruments Equipment: Optical box 11. Appendix A-1 96 Units and Prefixes 12. Appendix A-2 97 Fundamental Constants 13. Appendix B 98 Significant Digits and Uncertainties - 3 -

4 Experiment 1 Theory Units and Measurement The discipline of physics is an endeavor to understand the most fundamental principles of nature. We attempt to explain what can happen in nature in terms of quantitative relationships between motion, interactions, and states of matter. To do this, we must assign quantitative values to the properties of matter and describe their relationships through equations. Thus, physics is highly mathematical. In order to test quantitative relationships empirically, we must measure the quantities involved. Consequently, the primary focus of our first experiment is measurement. Each experiment will generate empirical results which we will compare to the predictions made by established physical theory. Units of Measurement All measurements are made in terms of units. When one reports a measurement it is not sufficient to just report a number. For instance, it would be meaningless to say that the width of an object is 5 without specifying whether the width is 5 inches or 5 centimeters or 5 meters or 5 miles. Each different type of measurement has a type of unit associated with it. Some of the most basic types of measurements are of length, of time, and of mass. Each of these has a unit or units of measurements associated with it. The basic units we will be using for each of these types of measurements are: Length: Time: Mass: meter (m) second (s) gram (g) Most of the other types of measurements can be expressed in units which are combinations of these three basic units. For other units of measurement see Appendix A. Sometimes we will want to work with larger or smaller versions of these basic units. For instance the mass of a typical person is about 75,000 g. So it might be better to write this in terms of kilograms (kg), 1 kg = 1000 g. So the mass of a typical person is 75 kg. The width of your little finger is about 0.01 m or 1 cm (1 meter = 100 centimeter). Another unit we might find useful is the millimeter (mm), 1 m = 1000 mm, 1 cm = 10 mm. Metric Prefixes It can be helpful to know the meaning of some of the prefixes used in the metric system. These prefixes make it easier to think about really large and really small numbers. You can find a list of these in Appendix A-1. There are other basic units that could be used for making measurements such as inches, feet, miles, etc, but we will be using only metric units (meters, grams, etc ) in our class. This is known as the Système International d'unités or SI Units

5 In addition to measurements of length, mass, and time, we can make other types of measurements such as area, volume, density, force, energy, and speed. These quantities can be expressed as combinations of the basic units. For instance, we can measure speed in miles/hour. The unit is miles divided by hours, or miles per hour. What would be an example of a metric unit of speed? Another example: the area of a rectangular region whose dimensions are (3 cm) (2 cm) would be 6 cm 2. The unit of area is cm 2, which is just cm cm. Volume In our experiment this week we will be measuring the volumes and masses of some objects and using those measurements to determine the object s densities. The volume of a block is equal to the product of its three dimensions (length width height). For example, the block pictured below has dimensions 2 cm 2 cm 3 cm so the volume is 12 cm 3. One unit of volume is cm 3. Imagine chopping it up into 12 smaller cubes, each 1 cm on a side. The volumes of each of the smaller blocks add together to create the volume of the larger block. Objects with irregular shapes also have volume associated with them. One way of measuring this volume would be to chop the object up into tiny cubes and add the volumes of each of the tiny cubes together to find the total volume. Can you think of a way to measure an irregularly shaped object s volume without chopping it up? 3 cm 2 cm 2 cm One unit of volume is cm 3. Some other units of volume are m 3 and mm 3. Another very useful unit of volume is the liter (L). 1 L = 1000 cm 3. Consequently, 1 milliliter (ml) = 1 cm 3. Density Density is another property of an object that can be determined by measurement. The density of an object or material is defined as the amount of mass per unit volume. So, 3 one unit of density would be g cm. We can determine the density of an object by measuring both the mass and the volume of an object and then dividing the mass by the volume. For example, suppose the 12 cm 3 block pictured before has a mass of 24 g. Then the density would be: density = mass/volume = 24g/12 cm 3 = 2.0 g/ cm 3. The density in g/ cm 3 represents the mass of each 1 cm 3 chunk of the block (assuming the density is uniform). Density is often a property of the material and does not depend on how much material 3 you have. For instance, lead has a density of 11 g cm and water has a density of

6 g cm gram. 3. The mass of one cubic centimeter of water was the original definition of the Measuring Instruments Different kids of measuring instruments are used to measure different kinds of quantities. For instance, one might use a meter stick to measure length, a stop watch to measure time, a scale to measure mass, and a thermometer to measure temperature. Different kinds of measuring instruments are used to measure quantities of differing sizes. It would be impossible to measure the size of a bacterium with a meter stick. You couldn t use the same instrument to weigh a truck as you do to weigh an ounce of water. What kinds of instrument could be used to measure distances of miles? Measurements and Uncertainties No measurement can ever be exact. The accuracy of a measurement (that is to say how close it is to the truth) will generally depend on the measuring instrument and the care taken by the measurer. Every measuring instrument has a limit on how precisely it can be read. For instance, a device with a digital display (like a digital watch) has a finite number of digits, limiting its precision. No finer gradation can be determined than the size of the least significant digit. Another example would be a meter stick which has a smallest division of 1 mm, or 0.1 cm. When we record a measurement we indicate our uncertainty in two ways. First, we only write down digits until we reach a digit we are unsure about. In other words, we should be sure about all the digits except the last one. Second, we indicate a range of possible values with a ± and an uncertainty estimate. This estimate is a judgment we make based on the measuring instrument and our experience. Based on my experience and the fact that the smallest division on a meter stick is 1 mm = 0.1 cm, I believe that any measurement I make with a meter stick is uncertain by at least ±0.1 cm. Other measuring instruments can give more precise, thus more accurate, measurements. A meter stick is limited by the size of its smallest division (0.1 cm). Vernier calipers, on the other hand, can be used to make much more precise measurements. However, with most increases in precision comes a limitation. In the case of the calipers their maximum range of measurement is about 20 cm. Uncertainties in calculated results Since the actual value of a measurement is uncertain, any result calculated from that measurement is uncertain. For example, suppose we measured the three dimensions of a wood block to be 8.3±0.1cm x 10.6±0.1cm x 5.2±0.1cm. That means that the volume of the block will be uncertain as well. Significant Figures or Digits - 6 -

7 We can use the concept of significant figures (or digits) to determine the approximate uncertainty of a calculated result like the volume. Every time you record a measurement, that measurement is recorded to a number of significant digits. Remember that you only record the measurement up to the first digit you are uncertain about. Often the number of significant digits will be the same as the total number of digits. This is true of our measurements of the wood block above. However this is not always the case. For rules on significant figures and rounding, as well as more on uncertainties, see Appendix B

8 Your Name: Lab Partner: Experiment 1 Work Sheet I. Mass Measure the mass of each of the seven objects listed in the following table. Record each measurement with an uncertainty estimate. Blocks Cylinders Object Aluminum Brass Wood Aluminum Brass Plastic 300 ml water Mass (g) Discussion: How do we measure the mass of 300 ml of water? II. Measuring Dimensions Measure the three dimensions of each of the three blocks with the meter stick and record each result in the following table. Meter Stick Measurements Blocks Aluminum Brass Wood Length (cm) ± 0.1cm Width (cm) ± 0.1cm Height (cm) ± 0.1cm Volume (cm 3 ) width length height Discussion: What is the equation for the volume of a block? - 8 -

9 Cylinders Aluminum Brass Plastic Diameter (cm) ± 0.1cm Height (cm) ± 0.1cm Volume (cm 3 ) diameter height Discussion: What is the equation for the volume of a cylinder? III. Measuring Volume Directly Discussion: How can we measure volume directly? Measure the volumes of the three cylinders and the Aluminum and Brass blocks directly (without using the ruler measurements). Fill in the uncertainty in your measurement. Direct Measurement of Volumes Aluminum Brass Plastic Block ± ml Cylinder ± ml Disscussion: Are the volumes measured directly exactly the same as those obtained from the dimension measurements (part II)? If not, are the values obtained by the two methods consistent given the margin of error in the direct measurements? - 9 -

10 IV. Density Compute the density of each of the objects from the measurements you have made. Remember: density = ( mass / volume ). Use the value for the volume obtained in part II. Record the result in the following table. Use your data to find the density of water and record the result in the density table. This is the experimental value; do not just use the theoretical value of 1.00 g/cm 3. Remember significant figures. Label each object F or S according to whether the object floats or sinks. Object Density (g/cm 3 ) Float/Sink Aluminum Block Cylinder Brass Block Cylinder Water Plastic Cylinder Wood Block Discussion: Do you see a relationship between density and buoyancy (the tendency to float)? Discussion: Look at the density values of your brass block and brass cylinder, are the two values exactly the same? Are the two values for the aluminum block and aluminum cylinder exactly the same? Should they be? What are the possible reasons that the two values do not agree?

11 V. Conclusion Discussion: Ships are made of steel, which is much denser than water. How can steel ships float? Write a short paragraph explaining what you learned in this experiment. What were the things you did not understand in this experiment?

12 Experiment 2 Variables, the Pendulum and Oscillations Theory Variables Often in physics we are interested how changing some aspect of a system changes its behavior. For instance, one might ask how changing the height from which an object falls changes the time it takes it to fall to the ground. What would you expect this relationship to be? As always, we are interested in the quantitative as well as the qualitative aspects of the problem. Any quantitative property of a system that can change is called a variable. In the case of the falling object, there are two variables of interest to us, the height from which it falls and the time it takes to reach the ground. In general there are two different types of variables that we can have in an experiment. There are variables that we have direct control over and whose values can be chosen before the experiment is begun. These are called independent variables. In the case of our falling object experiment, the height is an independent variable. The second type of variable is a variable whose value we do not know before doing the experiment. Its value depends on our choice of independent variables. This second type is called a dependent variable. In the falling object experiment, the time it takes the object to fall would be a dependent variable. In the falling object experiment, we could drop the same object from several different heights, and measure the time it takes to fall from each height with a stop watch. We could choose the heights we wanted to use before performing the experiment. Let s say we chose 5m, 10m, 15m, 20m, 25m, and 30m. If we perform the experiment we might get results like those shown in the table. Height (m) ± 0.1m Drop Time (s) ± 0.1s As you can see the drop time increase as the height increases. Is this consistent with our expectations? Graphs It is useful to display the relationship between two variables in a form of a graph. A graph is an x-y plot of the data points. Usually, the independent variable is plotted on the horizontal or x-axis and the dependent variable on the vertical or y-axis. When we make a graph, we choose the scale of the graph axis such that the data fill up most of the graph. Below is a graph of the falling object experiment data

13 Drop Time (s) Drop Time versus Height Height (m) The symbol I, represents the range of uncertainty in each data point. These are called error bars. Notice that each axis is clearly marked with the name of the variable, the unit, and the scale at regular intervals on the grid. These are all important elements that should be present on a graph. It is also worthy of note that the axis doesn t always have to start at zero. If you look at the drop time axis, you ll see that it starts at 0.5s not at 0s. Sometimes it is useful to graph some calculated result of the data. For instance you notice that the data points on the first graph don t fall near a straight line, but if instead we graph the square of the drop time versus the height we get: Drop Time squared (s 2 ) Drop Time Squared versus Height As you can see, the data points on the drop time squared versus height graph fall much closer to a straight line than those on the drop time versus height graph. Proportionality When the graph of two variables falls on (or very near, given uncertainties and errors inherent in any experiment) a straight line, we say that there is a linear relationship Height (m) between the two variables graphed. When the straight line can be fit to the data being graphed, we say that they are proportional to each other. So we would say that the Drop Time Squared is proportional to the Height from which the object is dropped since the data fall on (or very near) a straight line. When two variables are proportional to each other the ratio between them is constant. This is apparent for the Drop Time Squared versus Height data as shown in the following table. Height H (m) ± 0.1m Drop Time Squared D 2 (s 2 ) Ratio D 2 /H (s 2 /m) 2 ± 0.02s / m 5 1 ± 0.1m ± 0.2m ± 0.3m ± 0.4m ± 0.5m ± 0.6m

14 As you can see from the table, the ratio of the Drop Time Squared (D 2 ) divided by Height (H) is constant, within the allowed uncertainty. The ratio of two variables that are proportional is called the constant of proportionality. Slopes Drop Time Squared (s2) 2 ) Drop Time Squared versus Height Height (m) On a graph, this ratio is known as the slope of the line. To determine the constant of proportionality using a graph that you drew using graph paper, select two points on the line (these two points may not be data points since data points usually are not on the line due to experimental errors) where point 1 is (x 1, y 1 ) and point 2 is (x 2, y 2 ). Select points that intersect on the graph paper. The slope is defined as the change in y over the change in x (the rise over the run). In other words: slope = ( y2 y1 ) ( x x ) 2 1 Sometimes (0,0) is a valid first point but for example s sake, we will not use this point. The two points we will select are those that intersect on the graph paper and are circled. The values of the points can be read off the scales on the axis. Point 1 (2m, 0.5s 2 ) Point 2 (18m, 3.5s 2 ) 2 2 (.5s 0.5s ) s 2 slope = = = 0.19s / m 16m ( 18m 2m) Notice that the constant of proportionality found in the graph s slope matches that from the data table when the ratios were calculated individually. Graphs are preferred since they can forecast trends beyond the data we have collected. They are also preferred because they are a pictorial representation of the data and they make noticing trends easier

15 The Pendulum A pendulum consists of a bob of mass which is allowed to swing back and forth on the end of string (or other long thin arm A which is attached to a fixed point. L The pendulum can be characterized by several variables: the mass (m) of the bob, the length (L) of the arm, m the amplitude (A) or the swing angle, and the oscillation period (T). The oscillation period is defined as the amount of time it takes for the pendulum to swing from one extreme to the other and back again (one cycle). Notice that a single letter is chosen to represent each variable. These letters are useful as shorthand for referring to variables especially when writing down equations that relate them to each other. In an experiment involving the pendulum, which of these variables are independent? Which are dependent? Hypothesis Testing We often have an idea of what the outcome of an experiment will be before we do it. In fact, most experiments are designed with the goal of testing a particular theory about how nature behaves. A belief about what the result of an experiment will be, before the experiment is done, is called a hypothesis. Hypotheses can be based on common sense, what we have learned from others or from other experiments, or on some kind of intuition. When we have a hypothesis about how something will behave we need to design an experiment to test this hypothesis. The experiment we design should test the hypothesis as directly as possible, and from the results of the experiment we should be able to confirm whether what we believe was true or false. Sometimes, the experiment confirms that we were exactly right. Other times, our hypothesis is shown to be completely wrong. For example, Aristotle believed that heavier things fall faster than lighter ones. Galileo showed that, in general, all things fall at the same rate under Earth s gravity. In other instances, our experiments show us that our hypothesis, though not completely wrong, need adjustment

16 Your Name: Lab Partner: Experiment 2 Work Sheet I. Pendulum Hypothesis Today, you are going to make three hypotheses about the results of this experiment. It is best to make a hypothesis as simple as possible. Following are three questions about how the oscillation period (time for one cycle) of the pendulum changes when the different variables are changed systematically. In each case, you decide whether you think that the oscillation period will increase, decrease, or remain the same (meaning the variable does not affect the outcome). It won t matter whether your hypothesis comes out right or wrong, so just circle your best guess. 1. As we increase the amplitude (leaving the length of the arm and mass of the bob the same) how will the oscillation period change? (increase, decrease, remain the same) 2. As we increase the mass of the pendulum bob (leaving the length of the arm and amplitude the same) how will the oscillation period change? (increase, decrease, remain the same) 3. As we increase the length of the arm (leaving the mass of the bob and amplitude the same) how will the oscillation period change? (increase, decrease, remain the same) In this experiment, you will test each of these hypotheses. II. Oscillation Period and Amplitude protractor Attach the metal bob to the lab stand. Make the length of the pendulum about 25 cm. Thread the string through one of the holes on top and wrap (do not tie) around base of screw. Tighten the screw to hold the string in place. Start the pendulum swing with a small amplitude (read the angle off the protractor) and use the stop watch to measure how long it takes for the pendulum to go through ten cycles. ruler Discussion: Why measure for ten cycles and not just one?

17 Do three trials to reduce random uncertainties in the time. Record your values in the table below. Divide each trial by 10 to obtain the period of one oscillation. Find the average time for one oscillation of the three trials. To determine the margin of error ( ± ), subtract the smallest trial from the largest and divide by two. Record your results in the table. Small Amplitude: A S = Trial 1 Trial 2 Trial 3 Time for 10 oscillations (s) Time for one oscillation (s) Average time for one period (T S ): ± Repeat the previous procedure with a larger amplitude oscillation. (about twice as large). Record your results in the table Large Amplitude: A L = Trial 1 Trial 2 Trial 3 Time for 10 oscillations (s) Time for one oscillation (s) Average time for one period (T L ): ± Does the average time for one oscillation change when you increase the amplitude? If so, is the change larger than the margins of error allow for? Considering this, does your data confirm your hypothesis? Explain

18 III. Oscillation Period and Mass Measure the mass of the lead bob. Suspend the lead bob with a string length of 25cm and allow it to oscillate with amplitude of 20 o. Measure the time for 10 oscillations and enter it into the table. Repeat this twice for each bob. To find the margin of error subtract the smallest trial from the largest and divide by two. Mass (g) Time 1 (s) Time 2 (s) Avg time for 10 oscillations (s) Lead ± Brass ± Steel ± Wood ± Does the time for 10 oscillations change as you change the mass? If so, is there a consistent trend? Considering the margins of error is there a significant difference between the times? Do you confirm the hypothesis you made about how the period would change when the mass increases?

19 IV. Oscillation Period and Length Suspend two steel bobs from the lab stand, one with half the length of the other and pull both with the same amplitude. The only difference between these two bobs is the length of the arm. Set both pendulums to swing. Which has the longest period of oscillation? Look back at your hypothesis about the changes in length. Do your observations confirm your hypothesis? Explain. Now we will make a methodical series of measurements describing how the oscillation period changes when we change the length of the pendulum arm. As before, we will measure the time for ten oscillations but this time we ll vary the length of the pendulum each time. Use the steel bob and record the results in the following table. We will only perform one trial at each length. Use an amplitude of 20 o for each measurement. Length (cm) Ten periods (s) Period (s) Period 2 (s 2 ) Discussion: Which variable is the independent variable? Which axis should it be on? Discussion: Which variable is the dependent variable? Which axis should it be on?

20 * Graph the Period versus Length (T vs L). Make sure you have each of these parts of the graph: Title for graph Sensible scale for the axis (period scale of about 0 to 2.0 s and length scale from 0 to 80cm) Variable name on x and y axis with proper units Data points with error bars Draw the best fit curve (if it is a linear line, remember to use a ruler) Each student should attach a graph to this work sheet when it is turned in. * Graph the Period Squared versus the Length (T 2 vs L). The length scale will remain the same but it may help to change the scale of the period squared scale (about 0 to 3.0 s 2 ). Make sure you have each part of the graph excluding error bars for the period squared since this was not determined. Attach your graph to this work sheet when you turned it in. Discussion: Which graph fits a straight line? Find the slope of this line. Show your work on the graph itself. Slope of the line (experimental): From our knowledge of how the simple pendulum is expected to behave, we can predict what the value of the slope. According to the simple pendulum equation: T = 2π The variables can be rearranged to solve for the period squared (T 2 ) with all the constants grouped together: 2 2 4π T L g = This equation follows the equation for a straight line: y = mx + b where the slope is m, the y-intercept is b, y is the y-axis value and x is the x-axis value. Notice that the y-axis value is T 2, the x-axis value is L, and the y-intercept is zero so the slope must equal the constants (4π 2 /g). Calculate this constant where g=981cm/s 2 and π Slope of the line (theoretical): L g

21 To determine if your values agree it is useful to do a percent discrepancy (%D) calculation which determines how discrepant your value is. In general your percent discrepancy should be below 10% (in other words you are 90% correct and 10% in error). Calculate the percent discrepancy between the theoretical value of the slope and the experimental value of the slope. theoreticalvalue experimentalvalue % D = 100% theoretical value Before you performed this experiment, you formed several hypotheses about pendulum behavior. Now, you should have either confirmed or changed these ideas according to the results of your experiment. Write down what you now believe about the behavior of the pendulum. 1. As we increase the amplitude (leaving the length of the arm and mass of the bob the same) how will the oscillation period change? (increase, decrease, remain the same) 2. As we increase the mass of the pendulum bob (leaving the length of the arm and amplitude the same) how will the oscillation period change? (increase, decrease, remain the same) 3. As we increase the length of the arm (leaving the mass of the bob and amplitude the same) how will the oscillation period change? (increase, decrease, remain the same)

22 V. Conclusion Write a short paragraph explaining what you learned in the lab. What were the things you did not understand in this experiment?

23 Experiment 3 Uniformly Accelerated Motion Theory Speed and Acceleration When an object falls under the influence of gravity, it does not fall at a constant speed. The falling object s speed will continually increase as it falls toward the ground. An increase in speed over time is called acceleration. To further understand speed and acceleration let us look at a hypothetical experiment given in the previous lab. In this experiment, an object is dropped from a given height and the amount of time it takes to fall is measured with a stop watch. The data from this experiment is recorded in the following table. Height (m) ± 0.1m Drop Time (s) ± 0.1s As you might have expected, the higher the object when it is dropped, the longer it takes to reach the ground. There are some other features of the fall of the object under gravity that are worth noting. One way we can discover Figure 1 shows a graph of this data. new things about this experiment is by graphing the data. Notice how the line drawn through the data points curves upward. This means the object is accelerating as it falls. When an object is accelerating it moves faster and faster as it goes. What happens to your car as you get on the freeway is another example of acceleration. When you start out at the bottom of the entrance ramp to the freeway, you might be starting from as little as 0 miles/hour, but when you merge with the traffic on the freeway, you are traveling at freeway speeds (60 75 miles/hour). So somewhere in between your speed must have been increasing

24 Another way to represent the motion of the falling object is to graph the speed of the object as it falls to the ground. Figure 2 is a graph of the speed of the falling object versus time. You can see from the graph that the speed really does increase with time. Figure 2 Another thing that you might notice is that the line drawn through the data points is straight. This means that the acceleration is constant. All objects falling under the influence of gravity, near the surface of the earth fall with constant acceleration. In fact, the acceleration of all objects falling under gravity is the same no matter what the size or shape of the object. The air drag force exerted on lighter objects like feathers and sheets of paper does cause them to fall more slowly, but for larger more dense objects like books and bricks and people this effect is negligible at low speeds. Figure 3 is a graph of the acceleration of the falling object versus time. Note that the acceleration does not change over time. Also notice that the acceleration is about 5m/s 2. Look at Figure 2 and notice that the ball s speed increases by 5m/s every second. Acceleration (m/s 2 ) Accelertion of a dropped ball over time Time (s) As you might have noticed, speed and acceleration are measurable quantities, and in the course of this experiment you will have to measure them. You are probably already familiar with measurement of speed. As you drive your car you are constantly measuring your speed by looking at the speedometer on your dash board. Figure

25 In this experiment, we will be measuring speed in a more basic fashion. The speed of an object is the distance it travels (along a straight line) divided by the amount of time it takes to travel that time. For example, if you travel a distance of 120 meters over a period of four seconds (starting from rest): ( d f di ) save = ( t f ti ) s ave = average speed d f = final distance t f = final time d i = initial distance t i = initial time ( 120m 0m) 120m s ave = = = 30m s ( 4s 0s) 4s The unit for speed is meters per second (m/s). Notice that the average speed was 30 m/s. The instantaneous speed could have fluctuated up or down a great deal over that time period, but on average it was 30 m/s. The quantification of acceleration may be new to you, but acceleration is a measurable quantity just like speed. Acceleration is the change in the speed per unit time. In other words, the acceleration of an object is equal to the amount that the speed changes divided by the amount of time it takes it to change. The idea of average applies to the quantity of acceleration just like it does to speed. You can calculate acceleration just like you can calculate speed. For example, you accelerate in your car as you are getting on the freeway. You start from a speed of 0 m/s and accelerate up to 30 m/s (about 60 miles/hour), and you do this over a eriod of 15 seconds. Then your average acceleration is: a = a = ( s f si ) ( t t ) f a = acceleration s f = final speed t f = final time s = initial speed t = initial time i ( s f si ) ( t t ) f i = ( 30m / s 0m / s) ( 15s 0s) i i 30m / s = = 2m / s 15s The unit of acceleration is meter per second squared (m/s 2 ). In the example, the car increases its speed by 2 meters per second, every second

26 Your name Lab Partner Experiment 3 WORK SHEET PROCEDURE In this activity, you will drop a picket fence (a clear plastic strip with uniformly spaced opaque bands) through a photogate. The photogate beam is blocked by each opaque band and the time from one blockage to the next becomes increasingly shorter. Knowing the distance between the leading edge of each opaque band, the Science Workshop program calculates the average speed of the picket fence from one band to the next. A graph of average speeds versus time can give the acceleration due to gravity of the falling object. PART I: Computer Setup 1. Connect the Science Workshop interface to the computer, turn on the interface and then turn on the computer. 2. Connect the photogate s stereo phone plug to Digital Channel 1 on the interface. 3. Open the Science Workshop file titled Free Fall. The document will open with a Graph display that has plots of Position versus Time and a Table of Position versus Time. PART II: Equipment Setup The Science Workshop program has a 5.0 cm (0.050 m) spacing, leading-edge-toleading-edge, for the opaque bands on the picket fence. 1. Turn the photogate head of the accessory photogate sideways so that you can drop a picket fence vertically from above the photogate and have the picket fence move through the photogate s opening without hitting the photogate. Freely Falling Picket Fence Picket fence Photogate To Interface Base and support rod

27 Part III: DATA Recording 1. Prepare to drop the picket fence through the photogate beam. Hold the picket fence at one end between your thumb and forefinger so the bottom edge of the picket fence is just above the photogate beam. 2. Click the START button and then drop the picket fence through the photogate beam. Remember, data collection begins when the photogate beam is first blocked. 3. When the picket fence is through the beam, click STOP to end recording. 4. Record the value for the Time in the Data Table. 5. Calculate the average speed column by dividing the change in the distance (5.0 cm) by the time interval. The time interval is the difference between successive times. 6. Calculate the time at average speed column by averaging the two successive times together. 7. Make a graph from the Data Table, Average speed versus Time at average speed. Time (s) Distance (cm) Time at average speed (s) Average Speed (cm/s) slope of velocity versus time = (from Graph) acceleration = (theoretical value)

28 IV. Questions 1. How does the slope of your velocity versus time plot compare to the accepted value of the acceleration of a free falling object (g = 980 cm/s 2 )? Theoretical value - experimental value % difference = x100% Theoretical value 2. What factors do you think may cause the experimental value to be different from the accepted value?

29 V. Conclusion Write a short paragraph explaining what you learned in this experiment. What were the things you did not understand in this experiment?

30 Experiment 4 Levers Theory Levers Levers are simple machines that allow you to lift or move something you otherwise would not be able to move. You have all heard the phrase apply leverage in many different contexts, and most of you have used a lever of some type or another. When you use a wrench to tighten or loosen a bolt, you are using a lever. When you use a wheelbarrow to carry or dump a heavy load, you are using a lever, and when you use a crow bar to pry open a crate, you are using a lever. In each of these cases the lever allows you to lift or move something you would not be able to lift or move with your bare hands or fingers. This can happen because a lever allows you to exert more force than you could by simply pushing, pulling or lifting. Pictured below is a common type of lever. Force applied to end of lever (F2) In general a lever consists of a long rigid bar, and a fulcrum. The fulcrum is the point about which the bar pivots. The load is whatever is to be moved. The load arm is the distance from the fulcrum to the load, and the lever arm is the distance from the fulcrum to where the force (push, pull or lift) is applied. The lever above could be used to lift a mass that was too heavy to be lifted with arms and legs alone. Sometimes the load and the applied force are on the same side of the fulcrum, as pictured below. This is true in the case of the stapler and wheel barrow. In either case, the leverage or mechanical advantage that you gain by applying a lever increases as the lever arm increases and decreases as the load arm increases. So, in general,

31 you want the lever arm to be as large as possible and the load arm to be as short as possible. Work At first it may seem that the lever violates Newton s Third law. This states that for every action there is an equal and opposite reaction. How can the force exerted on the load be larger than the force exerted by the person? We can reconcile the lever to Newton s laws by realizing that there are forces other than the force exerted at the lever arm at work. The fulcrum also exerts a force on the bar which is transferred to the load. For this reason it is necessary that the fulcrum be firmly secured to the earth or some other very massive object. If the fulcrum is not firmly secured the lever may not work. As students of physics we are not only interested in the qualitative aspects of how the lever works. We are also interested in the quantitative aspects of the lever. One might ask how much mass can be lifted with a given lever arm and load arm. The best way to describe this quantitatively is to use the concept of Work. The amount of work done by an applied force is equal to the force applied times the distance moved. For example if one lifts a 1 kg mass to a height of 1 m the work against gravity is the product of the gravitational force and the distance moved. Work = Force x Distance = 9.81 m/s 2 x 1 kg x 1 m = 9.81 kg m 2 /s 2 = 9.81 Joules In the case of the lever the work done on the load is equal to the work done by the applied force at the lever arm. For example if 2 m the load arm is 1 m long and the lever arm is 2 m long and the load has a mass of 1 kg, and the load is lifted one meter, then the amount of work done on the load is 9.81 Joules. However, when the load arm moves 1 m the lever arm moves two meters, so the force applied at the lever arm must be only half of that applied to the load. The force applied to the lever arm is (1/2)(9.81 kg m/s 2 ) = 4.91 kg m/s 2. The unit of force kg m/s 2 is called a Newton and abbreviated N. In general, the work done on the load is equal to the work done by the applied force at the lever arm. Since the work done by a force is equal to the force multiplied by the distance moved: W1 = W2 F1 D1 = F2D2-31 -

32 Consequently, F1/ F2 = D2/ D1 The lever and load arms and the vertical movements are geometrically proportional. So the ratio of the load force to the lever arm force is equal to the inverse ratio of the arms radii. Balance F1/ F2 = r2/ r1 The relation above is the basis for the balance. You all know that if you suspend equal weights at equal distances from the fulcrum the result will be balance. Neither mass will rise nor fall. If you move one of them farther out on the rod it will begin to fall and the other will rise. One thing that you may not realize is that you can balance a heavy object with a lighter object if the lighter object is farther from the fulcrum. This is a direct consequence of the relationship of the force to arm length derived in the previous section. The force of gravity pulls down on each of the masses. The first mass, m1, at length r1 from the fulcrum experiences a gravitational force of Fg1 = m1g. The second mass, m2, experiences a gravitational force Fg2 = m2g. If the masses are balanced then the masses are at rest, which means that the force of gravity is being counteracted by the force exerted on each mass by the rod. We know from the earlier discussion that the force exerted on m1 by the rod, F1, is related to the force exerted on m2 by the rod, F2. F 1 F 2 = r 2 r

33 We also know that F 1 and F 2 are equal and opposite to the gravitational force on the masses. F 1 = F g1 = m 1 g F 2 = F g2 = m 2 g Consequently, there is a simple relationship between the masses and the distances to the fulcrum. m 1 r 1 = m 2 r

34 Your Name: Experiment 4 Work Sheet Lab Partner: I. Balance Remove the two mass holders from the bar. Use the scale to measure the mass of each of the two hanging masses along with its corresponding mass holder. Note that the value will be larger than what is printed on the hanging mass because of the weight of the mass holder. Small Mass: m 1 = Large Mass: m 2 = Then find the ratio of the two masses, m2/m1. Record your result as a decimal number. m 2 m 1 = Place the smaller mass, m 1, at r 1 =10 cm from the fulcrum (0 cm) and find the point r 2 on the other side where the larger mass, m 2, balances it. Repeat this procedure with the smaller mass at r 1 = 12, 14, 16, 18, and 20 cm from the fulcrum. Make sure that the middle of the bar (0 cm) is always at the fulcrum. Record your results in the following table. Find the ratio of r 1 r 2 for each pair of measurements and record the result in the third column of the table as a decimal number. r1 (cm) r 2 (cm) r 1 r 2 Table 1 for balance points Discussion: What is the relationship between m 2 and r 1? Does your data m 1 r 2 show this?

35 Repeat the above procedure with a different pair of (unequal) masses. Then find the ratio of the two masses. Small Mass: m 1 = Large Mass: m 2 = m 2 m 1 = Discussion: What do you expect the value of r 1 r 2 to be? Table 2 for balance points r1 (cm) r2 (cm) r 1 r 2 Discussion: Compare the values of r 1 recorded in the table to the value of m 2. Do your r 2 m 1 results show that m 2 = r 1? m 1 r

36 II. Conclusion Write a short paragraph explaining what you learned in this experiment. What were the things you did not understand in this experiment?

37 Experiment 5 Conservation of Energy Theory Conservation of Energy This experiment will demonstrate the law of conservation of energy. The law of conservation of energy states that energy can neither be created nor destroyed. So in an isolated system (a system is a collection of bodies, an isolated system is a collection of bodies that is not acted on by anything external to the system) the total amount of energy never changes. Even though the total amount of energy never changes, energy can be transferred from one body to another, and transformed from one form to another. There are many forms of energy: kinetic energy, gravitational energy, thermal energy, elastic energy, chemical energy, electrical energy, and nuclear energy. In this experiment, you will only deal with kinetic energy, gravitational energy and elastic energy. There will be other forms of energy in the system of bodies you will be working with, but those forms of energy will not be changing in significant amounts to be considered. Kinetic Energy Kinetic energy is the energy of motion. Any object that is in motion has kinetic energy. In Newtonian physics, the amount of kinetic energy, K that a body has is given by: KinE = (1/2) mass (speed squared) = (1/2)mv 2 where m is mass and v is speed. Notice that the kinetic energy is proportional to the mass and proportional to the speed squared. m speed = v KinE = (1/2)mv 2 Units of Energy You will be measuring masses in kilograms (kg), lengths in centimeters (m) and time in seconds (s). So, for example, a mass of 10.0 kg moving at a speed of 4.0 m/s has a kinetic energy of: KinE = (1/2)mv 2 = (1/2) (10.0kg)(4m/s) 2 = 80 kg m 2 /s 2 = 80 Joule = 80 J The unit, kg m 2 /s 2, is called a Joule (J). So the Kinetic energy is K = 80 J. Another unit of energy is the erg. 1 erg = 1 g cm 2 /s

38 Gravitational Energy m h GravE= mgh Gravitational energy (often called gravitational potential energy) is the energy associated with gravity. Gravitational energy is associated with the height of an object. Notice that Gravitational energy is proportional to the mass and proportional to the height. The amount of gravitational energy, GravE, that a body has (actually, we think of the energy being shared between the Earth and the body) is given by: Gravitational energy = weight of the body the height of the body Remember: Weight = mass 9.8 m/s 2 = mg GravE= mgh where m is the mass of the body, g is gravitational acceleration (9.8 m/s 2 ) and h is the height. Elastic Energy Elastic energy (often called elastic potential energy) is the energy associated with stretching or compressing a spring (or stretching or compressing anything that can be stretched or compressed). The amount of elastic energy in the spring depends on how much the spring is stretched or compressed. Hooke s Law Most springs obey Hooke s Law, which means that the force required to stretch the spring is proportional to amount that it is stretched. For a spring that obeys Hooke s Law the force, F, that must be exerted on the spring to make it stretch a distance x is given by:

39 Force exerted on spring = (spring constant) (amount of stretch) F = kx where k is the spring constant, and x is the amount of stretch. We will use lower case k for the spring constant and upper case K for kinetic energy. The amount of stretch, x, is the equal to the length of the spring when it is stretched minus the length of the spring when it is not stretched. For a spring that obeys Hooke s Law, the amount of elastic energy, ElastE, stored in the spring is: Elastic energy = (1/2) (spring constant) (amount of stretch squared) Mechanical Energy ElastE = (1/2) kx 2 You will be measuring the kinetic energy, the gravitational energy, and the elastic energy of a mass oscillating up and down on a spring. There will be other forms of energy in your experiment that you will not measure (i.e. Thermal energy). However, these other forms of energy will not change substantially during your experiment. You will treat the sum of the kinetic, gravitational and elastic energies as if it were the total energy in the system. We will call the sum of the kinetic, gravitational and elastic energies the total mechanical energy: Total Mechanical Energy = Kinetic Energy + Gravitational Energy + Elastic Energy E total = KinE +GravE + ElastE You will measure the total mechanical energy at three points in the oscillation of the mass on the spring, at the top, in the middle and at the bottom. What you will find if you do the experiment carefully is that the total mechanical energy doesn t change appreciably throughout one oscillation of the mass on the spring

40 Your Name Lab Partner Experiment 5 Work Sheet I. Measurements 1. Middle Height: Allow the kg mass to hang freely from the spring. Stop it from oscillating (bouncing) so that it hangs at rest. While its hanging at rest measure the height of the bottom of the mass above the table. Measure all heights and lengths in meters. This is the middle height, H M. Record your measurement below: (you will need to convert all length measurements to meters) H M = m 2. Position the photogate so that mass hangs in the middle of the infrared beam both vertically and horizontally. Middle Height H M 4. Timer Setup: Make sure that the timer is plugged in and the power strip is on.the timer setting should be as follows. The timer should be set to GATE. The memory switch should be on. The precision switch should be set to 0.1 ms. As shown in the photo below. Use the red reset button to set the timer to zero before every measurement. 0.1 ms Gate Reset to zero Memory - on

41 4. Top Height: Lift the kg mass by the stem until the spring is unstreched. Hold the mass in the position where it barely touches the spring but does not stretch it. Measure the height of the bottom of the mass above the table. This is the top height, H T. Record your measurement below: H T = m 5. While holding the mass by the stem so that the spring is unstretched. place the meter stick near the mass so that you will be able measure the bottom most height that the kg mass reaches while it is oscillating. Reset the time to zero by pushing the red reset button. Top Height H T 6. Drop the kg mass. Within first two or three bounces measure the lowest point that the bottom of the mass reaches. This is the bottom height, H B. Make sure that the mass doesn t hit anything before you measure the bottom height. Record your measurement below: H B = m 7. Record the time displayed on the timer, t, below. The time is in seconds. This is the amount of time that it takes for the kg mass to pass through the timer the first time it goes through. Bottom Height H B t = 8. You will also need to know the length of the body of the kg, L, mass to determine the speed in the middle. Measure L and record your measurement below: L = m Length of the mass L mass

42 Spring Constant In order to find the elastic energy, you will first need to find the spring constant of the spring. The spring constant is the equal to the force exerted by the spring divided by the amount that it is stretched. The weight of the kg mass is: Weight = mass grav. acceleration = How big is the force exerted by the spring on the kg mass when the mass is hanging at rest in the middle? F = The amount that the spring is stretched when the mass is hanging in the middle is the difference of the top and middle heights: Stretch = H T -H M = The spring constant is the force exerted by the spring divided by the stretch: Energy at the Top Spring Const = F/Stretch = Gravitational: Calculate the gravitational energy, GravE, of the kg mass at the top. GravE = Mass gravitational acceleration H T = Kinetic: What is the speed of the kg mass at the moment you release it? What then is the kinetic energy, KinE, of the mass at the top when you release it? KinE = Elastic: How much is the spring stretched when you release the kg mass? What then is the elastic energy, ElastE, of the spring at the top? ElastE = Total: What is the total gravitational+kinetic+elastic energy at the top? Top Total = GravE+KinE+ElastE=

43 Energy in the Middle Gravitational: Calculate the gravitational energy, GravE, of the kg mass in the middle. GravE = Mass gravitational acceleration H M = Kinetic: As the kg mass goes through the timer it moves a length, L, in a time, t. Use the measured values to find the speed (avg. speed) in the middle: speed = L/t= Use the speed and the mass to find the kinetic energy in the middle? KinE = (1/2) mass (speed) 2 = Elastic Energy: From the stretch and the spring constant you can find the elastic energy: Stretch = H T -H M = ElastE = (1/2) (Spring Const) (Stretch) 2 = Total: What is the total gravitational+kinetic+elastic energy in the middle? Middle Total = GravE+KinE+ElastE= Energy at the Bottom Gravitational: Calculate the gravitational energy, GravE, of the kg mass at the Bottom GravE = Mass gravitational acceleration H B = Kinetic: What is the speed of the kg mass at the moment it reaches the bottom? What then is the kinetic energy, KinE, of the mass at the moment it reaches the bottom? KinE = Elastic Energy: The amount that the spring is stretched when the mass is hanging at the bottom is the difference of the top and middle heights: Stretch = H T -H B = From the stretch and the spring constant you can find the elastic energy ElastE = (1/2) (Spring Const) (Stretch) 2 = Total: What is the total gravitational+kinetic+elastic energy at the bottom? Bottom Total = GravE+KinE+ElastE=

44 Comparisons According to the law of conservation of energy, the total energy should be the same at the top, the middle and the bottom. Is the total energy the same at all three places? Find the percent discrepancy between the Top Total and the Middle Total energies. Use the Top Total as the Theoretical value. Middle %D = Find the percent discrepancy between the Top Total and the BottomTotal energies. Use the Top Total as the Theoretical value. Bottom %D = Given the size of the discrepancies, do you think there is a significant difference between the total energies at the top, the middle and the bottom? kg Mass: Repeat the procedure for the kg mass 1. Middle Height: H M = m 2. Position the photogate so that mass hangs in the middle of the infrared beam both vertically and horizontally. 4. Timer Setup is the same 3. Top Height: H T = m 5. While holding the kg mass at the unstretched position. Reset the time to zero by pushing the red reset button. 6. Drop the kg mass. Measure H B = m 7. Time on timer: t = 8. Length of the body of the kg mass: L = m

45 Energy at the Top Gravitational: GravE = Mass gravitational acceleration H T = Kinetic: KinE = Elastic: ElastE = Total: Top Total = GravE+KinE+ElastE= Energy in the Middle Gravitational: GravE = Mass gravitational acceleration H M = Kinetic: speed =L/t= KinE = (1/2) mass (speed) 2 = Elastic: Stretch = H T -H M = Elastic Energy: Use the same spring constant as in the previous sections ElastE = (1/2) (Spring Const) (Stretch) 2 = Total: What is the total gravitational+kinetic+elastic energy in the middle? Energy at the Bottom Middle Total = GravE+KinE+ElastE= Gravitational: GravE = Mass gravitational acceleration H B = Kinetic: KinE = Elastic Energy: Stretch = H T -H B = Elastic Energy: Use the same spring constant as in the previous sections ElastE = (1/2) (Spring Const) (Stretch) 2 = Total: What is the total gravitational+kinetic+elastic energy at the bottom? Bottom Total = GravE+KinE+ElastE=

46 Comparisons According to the law of conservation of energy, the total energy should be the same at the top, the middle and the bottom. Is the total energy the same at all three places? Find the percent discrepancy between the Top Total and the Middle Total energies. Use the Top Total as the Theoretical value. Middle %D = Find the percent discrepancy between the Top Total and the Bottom Total energies. Use the Top Total as the Theoretical value. Bottom %D = Given the size of the discrepancies, do you think there is a significant difference between the total energies at the top, the middle and the bottom?

47 II. Conclusion Write a short paragraph explaining what you learned in this experiment. What were things you did not understand in this experiment?

48 Experiment 6 Specific Heat Theory The First Law of Thermodynamics The total energy of a system remains constant. The first law of thermodynamics is a statement of conservation of energy. If an object A comes into contact with an object B, where object A has a higher temperature (and therefore more thermal energy), the thermal energy (or heat) gained by one object will equal the thermal energy lost by the other object. Which object loses thermal energy and which one gains thermal energy is determined by the second law of thermodynamics. The Second Law of Thermodynamics The entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium. The second law of thermodynamics is a statement of order in the system. Over time, entropy (or disorder) increases. Heat always flows from a hotter object to a cooler object because the thermal energy becomes more disordered in this process. The thermal energy will flow until the system reaches a state of thermal equilibrium at which point the two objects reach the same temperature. The hot body loses precisely the same amount of heat as the cold body gains, in accordance with the First Law of Thermodynamics. The Third Law of Thermodynamics As a system approaches absolute zero of temperature, all processes cease and the entropy of the system approaches a minimum value. The minimum value of entropy is zero, although no system can actually reach this state. As a consequence, no heat engine can ever be 100% efficient. Specific Heat The specific heat of a material is defined as the amount of heat we need to add in order to raise the temperature of a given mass of material by one unit of temperature (normally 1 C or 1K). Because each material has its own specific heat some materials change their temperature more quickly and easily than others. Water, for example, has a specific heat of 4200 J/kg o C. This means that you would need 4200 joules of energy to heat one kilogram of water a mere one degree. By way of comparison, to raise the temperature of one kilogram of aluminum by one degree Celsius you need only 900 joules of energy, because its specific heat is 900 J/kg C. Other things being equal, the different specific heats mean that aluminum will change temperature a lot faster than water

49 object A hot object B + cool = object A loses heat object B gains heat. The second law of thermodynamics states that heat will flow from the hotter object (object A) to the colder object (object B). This process will continue until the two objects have the same temperature, then the flow of heat will stop. The heat lost by object A will equal the heat gained by object B as long as no heat is transferred from the two objects to the environment surrounding the objects. m A = mass of A c A = specific heat of A Q A = heat lost by A T Ai = initial temperature of A T Af = final temperature of A m B = mass of B c B = specific heat of B Q B = heat lost by B T Bi = initial temperature of B T Bf = final temperature of B The heat lost, mass of the object, specific heat of the object and the initial and final temperatures are related by the following formula. Q A = m A c A (T Ai T Af ) Object A is losing heat so the initial temperature will be greater than the final temperature. Q B = m B c B (T Bf T Bi ) Object B is gaining heat so the final temperature will be greater than the initial temperature. By the first law of thermodynamics, the heat lost equals the heat gained so Q A equals Q B. Q A = Q B m A c A (T Ai T Af ) = m B c B (T Bf T Bi ) Since heat will stop flowing when object A and object B have reached the same temperature, the final temperature of object A and object B will be the same. This gives us: T Af = T Bf = T f m A c A (T Ai T f ) = m B c B (T f T Bi ) We will use this relationship to determine the specific heats of different materials

50 Your Name Lab Partner Experiment 6 Work Sheet I. Specific Heat First, measure the masses of the empty dry calorimeter (Styrofoam cup), and each of the three metal samples (lead, copper, and aluminum) and enter the values below. Then put the three masses in the boiling water with the attached threads hanging out (so that they can be removed from the water safely). Leave the samples in the boiling water for several minutes; we can assume that they reach thermal equilibrium with the boiling water. The initial temperature of the samples will be 100 C. For Aluminum: Fill the calorimeter with just enough cold water to cover the aluminum sample. Do not put the aluminum sample in yet. Measure the mass of the empty, m cal, and filled, m cal+water, calorimeter. m cal = g water heater Calorimeter (foam cup) m cal+water = g Take this mass and subtract the mass of the empty dry calorimeter and you will get the mass of the water. m cal+water m cal = M water = g Measure the mass of the Aluminum cylinder, M Al and record the result in the table Record the temperature of the water in the calorimeter. Add the Aluminum cylinder to the calorimeter. Gently move the Aluminum cylinder up and down to circulate the water in the calorimeter being careful not to let the cylinder touch the bottom of the calorimeter or to let the cylinder come above the surface of the water. Also stir the water gently with the thermometer. The temperature reading on the thermometer will rise as heat flows from the Aluminum cylinder to the water. Keep your eye on the thermometer and record the final temperature. It should take a few minutes to reach thermal equilibrium

51 M water (g) M Al (g) T water (in cal) ( o C) T Al (in boilier) ( o C) T f ( o C) Aluminum (Al) When you have recorded all your values, calculate the specific heat C Al for Aluminum. Compare your calculated values with the theoretical values. Remember that the specific heat for water ( C water ) is 4200 J/kg o C. M Al C Al (T Al T f ) = M water C water (T f T water ) C Al exp (J/kg o C) C Al theo (J/kg o C) %D Aluminum (Al) 900 Repeat the procedure for the copper and the aluminum and calculate C Cu for copper, and C Al for aluminum. Use fresh water for each object. For Copper: m cal = g m cal+water = g Take this mass and subtract the mass of the empty dry calorimeter and you will get the mass of the water. m cal+water m cal = M water = g M water (g) M Cu (g) T water (in cal) ( o C) T Cu (in boilier) ( o C) T f ( o C) Copper (Cu) M Cu C Cu (T Cu T f ) = M water C water (T f T water ) C Cu exp (J/kg o C) C Cu theo (J/kg o C) %D Copper (Cu)

52 For Lead: m cal = g m cal+water = g Take this mass and subtract the mass of the empty dry calorimeter and you will get the mass of the water. m cal+water m cal = M water = g M water (g) M Pb (g) T water (in cal) ( o C) T Pb (in boilier) ( o C) T f ( o C) Lead (Pb) M Pb C Pb (T Pb T f ) = M water C water (T f T water ) C Pb exp (J/kg o C) C Pb theo (J/kg o C) %D Lead (Pb) 130 Discussion: Why do we use a Styrofoam cup instead of a plastic or metal cup? Discussion: Did your experimental value agree exactly with your theoretical value? Why not? Discussion: Was the second law of thermodynamics shown to be true?

53 II. Conclusion Discussion: Which element caused the water temperature to increase the most? According to what you have learned about specific heats, does this make sense? Write a short paragraph explaining what you learned in this experiment. What were things you did not understand in this experiment?

54 Experiment 7 Waves Theory Waves Wave phenomena are observed in a variety of everyday experiences. The most obvious examples of waves are ripples on the surface of water. You ve all seen the way the ripples propagate away from the point where a rock is dropped into the water. There are many other examples of familiar phenomena which are not as obviously wave related. The most important of these are sound and electromagnetic waves. Electromagnetic waves include such things as light, radio, microwaves, infrared radiation, ultraviolet, and X-rays. When we study waves, we are thinking about some sort of disturbance (like the rock falling into the water) that propagates away from the point of origin. For sound waves the source might be a loud-speaker or a musical instrument, or a person s vocal chords. For electromagnetic waves the source might be a transmitting antenna (radio), or a light bulb (light). Waves do not travel infinitely fast; rather, they have a finite, characteristic speed. Electromagnetic waves move at the speed of light (3 x 10 8 m/s) which is extremely fast. Sound moves at the speed of sound which is about 340 m/s. If you hear echoes, you are hearing evidence of the finite speed of sound. Waves on the surface of water move at different speeds depending on the wavelengths and depth of the water. Transverse and Longitudinal Waves There are two basic types of wave disturbances: transverse and longitudinal. Transverse waves are waves in which the direction of the disturbance or movement is perpendicular to the direction of motion of the wave. An example of a transverse wave would be the side to side motion of a plucked string. In longitudinal waves, the disturbance is along the direction of motion. Sound is an example of a longitudinal wave. A sound wave s disturbance changes the density of the air through which it moves. As the sound wave passes, the density increases and then decreases slightly. The compression of the air is in the direction of motion. At first it would seem that water waves are transverse waves, but they are actually a combination of the two. In a water wave, the water actually moves in small circles. So in a water wave there is both movement in the direction of motion and movement perpendicular to the direction of motion. Wavelength and Frequency Waves are usually characterized by their wavelengths and/or their frequencies. Often waves come in trains of peaks and troughs that repeat over and over along the length of the wave

55 Amplitude A (cm) How high the wave is. Wavelength λ(cm) How long the wave is. The distance from one peak to the next peak, or from one trough to the next trough (in other words, the distance at which the pattern begins to repeat itself) is called the wavelength. We often use the Greek symbol, lambda λ, to represent the wavelength. Another characteristic of the wave is its frequency. Imagine that you are floating on the surface of the water as waves pass by. As you float you move up and down with an oscillating motion. This oscillation has a characteristic period, which is the amount of time it takes to go through one oscillation. Another way to quantify the rate of the oscillation is the frequency of oscillation. The frequency is the number of oscillations that take place in a given amount of time. We will use f to represent frequency. The frequency is the reciprocal of the period. f = 1/Period In other words, if the period of oscillation is 2.0 seconds (2.0 s) then the frequency is 0.5 s -1 or 0.5 Hz. The unit of frequency is called the Hertz (Hz). 1 Hz = 1 s -1. If you look at a radio tuner, you will notice that the frequencies of AM radio broadcasts range from about 540 to 1500 khz, where a khz = 1000 Hz. FM radio broadcasts range in frequency from about 90 MHz to 110 MHz, where one MHz is 1,000,000 Hz. You can see that radio frequencies are very high. Audible sound waves have much lower frequencies. People can hear sounds within the frequency range of about 20 Hz to 20,000 Hz. As you get older your ability to hear the higher frequencies diminishes; most adults cannot hear a tone of 20,000 Hz. The pitch of a musical note corresponds to the frequency of the sound wave. For instance, middle C on the piano corresponds to a frequency of about 260 Hz. The first A above middle C corresponds to a frequency of 440 Hz. The wavelength and the frequency are related to the wave speed. This can be shown easily in the following illustration of a moving water wave and a stationary buoy

56 X v Time: 0 X v Time: 0.5T X v Time: T λ As you can see, the wave moves one wavelength, λ, during one oscillation period, T. Consequently, the wavelength must be equal to the product of the wave speed, v and the period. λ= vt Since the frequency, f, is the reciprocal of the period, T, the wave speed must then be equal to the product of the wavelength and the frequency λf = v Waves of many different frequencies can be present in the same place at the same time. For example, often in music there is more than one note being played at a time. The radio waves from each of the different available radio stations are passing through the air at the same time. Your tuner just picks out the one that you choose and filters out all the others. When waves of different frequencies or waves traveling in different directions meet, their amplitudes simply add together. This property is called superposition. For instance a

57 high frequency wave and a lower frequency wave traveling together might look like the illustration below. Two waves of the same wavelength traveling in opposite directions also add together this way. Often waves become trapped in a region because they reflect off the boundaries of the region. You have all seen how water waves reflect off the sides of a swimming pool, and you have all heard an echo. These are both examples of reflection. Reflection doesn t occur only where there is a hard boundary inhibiting the passage of the waves. It can also occur where there is an abrupt change in the medium that is transmitting the wave. An example of this is the reflection you see in a transparent piece of glass. This reflection occurs because the speed of light is slower in the glass than in the air. Standing Waves Incident wave Reflected wave Another type of wave that can be made is the deflection on a stretched string. You may have noticed that if you stretch a rope tight and then move one of the ends quickly, it sends out a ripple much like the ripple on the water. If you stretch the string tightly between two fixed points, waves traveling along the string will be reflected back along the string in the other direction. Constructive interference Destructive interference These reflected waves will then be added to the oncoming waves, and they will continue on to be reflected back at each end. This addition of waves is called interference. There are certain wavelengths at which the waves traveling in the two directions will add together coherently. When this happens, there are some points on the string, called nodes, where they will always cancel each other out exactly. At a node, the string is

58 stationary. There are other places where the waves will add together to produce an oscillation twice as large as the individual waves would produce. We call these points anti-nodes. When such waves are made on the string it is called the condition of resonance. Remember that this condition depends on the wavelength; it is equivalent to say that it depends on the frequency. Such a wave is called a standing wave, and the frequency used to make it happen is called a resonant frequency. The string stretched tight between two fixed points constitutes a resonant cavity. Other examples of resonant cavities are organ pipes and wind instruments in general. These are examples of acoustic (sound wave) resonant cavities. A guitar string is another example of a resonant cavity. The inside of a laser tube is an optical resonant cavity. For the stretched string, the condition for resonance is that the length of the string, L, be some multiple of twice the wavelength, λ. ` λ = 2L/n (n = 1, 2, 3, 4 ) Some of the standing waves on a stretched string would look something like this: λ= 2L n=1 λ= L n=2 L= resonant cavity length (cm) λ= 2L/3 n=3 node λ= L/2 n=4 antinode As shown in the illustrations above, standing waves do not move back and forth. Instead, the standing waves oscillate back and forth in place, but the amplitude is different at different points on the string. Remember that what we mean by amplitude is the size of the disturbance

59 Your Name Lab Partner Experiment 7 Work Sheet In this experiment we will generate some standing waves on a stretched string, we will measure some resonant frequencies of the stretched string, and we will see how changing the tension and the length of the string change each of the resonant frequencies. I. The Apparatus Attach the 200 g mass to the end of the string. Pass the string over the pulley and attach the other end to a fixed point on the lab stand. Resonant cavity length L wave driver ** tension on string (T) frequency signal generator m frequency knob Connect the signal generator to the wave driver with the two cables provided. Attach the drive rod of the wave driver to the string. Measure the length of the stretched string, L 1, from the drive rod to the pulley. II. Standing Waves amplitude knob L 1 = gravitational force ( F g =mg) F g =T Turn the signal generator on. Decrease the frequency until you find a resonant mode. Record the frequency displayed on the signal generator and the corresponding resonant mode number, n, in the following table. Repeat this for the other modes of the string shown above

60 Trial A Tension =.200 kg 9.8 m/s 2 = 1.96 N Length = L 1 n λ (cm) f (Hz) v (cm/s) Repeat the experiment with a different tension on the string by replacing the 200 g mass with the 500 g mass. This changes the tension on the string from 1.96 N to 4.9 N. Trial B Tension =.500 kg 9.8 m/s 2 = 4.9 N Length = L 1 n λ (cm) f (Hz) v (cm/s) Repeat the experiment with a different resonant cavity by shortening the string to half the original length. Replace the 500 g mass with the 200 g mass to bring the tension back to the original 1.96 N. Trial C L 2 = Tension =.200 kg 9.8 m/s 2 = 1.96 N Length = L 2 n λ (cm) f (Hz) v (cm/s) Discussion: How does the tension affect the velocity of the wave? How does the length affect the velocity of the wave?

61 III. Conclusion Discussion: When you tighten (increase the tension) a guitar string, its frequency of vibration (resonant frequency) increases. Is this consistent with the results of this experiment (Trial A vs. Trial B)? Explain. Discussion: Musical instruments with shorter lengths usually make higher pitches. Is this consistent with the results of your experiment (Trial A vs. Trial C)? Explain. Write a short paragraph explaining what you learned from this experiment. Was there anything that you did not understand about this experiment?

62 Experiment 8 Electricity Theory Electricity Electric power is such an integral part of our lives that most of us could not imagine life without it. So it is important that we understand some of the basic principles of electricity. Electricity involves the flow of charged sub-atomic particles called electrons through wires or other conductors. Electrons are too small to be seen, and in general, the flow of electrons is invisible, but electric power provides the energy that runs electric motors, and all other electric appliances. In addition to energy to move things around electricity provides the energy that is converted into light in light bulbs. Electricity also allows us to transmit and receive electromagnetic signals (radio and TV waves), and convert them back to sound and pictures. Inside a television or computer monitor, other electrical devices use more electrons to paint pictures on the tube. The extremely small and fast arrays of switches (chips) that are the heart of modern computers, cellular phones, calculators, engine controls in automobiles, etc. are also examples of electric circuits. Electromagnetic Fields Electrons have a special property. We say that they have electric charge. Charged particles interact with each other (exert forces on each other) through electromagnetic fields. Electromagnetic fields cause forces that act at a distance, much like the gravitational force of the earth pulls on the moon. There are two kinds of electromagnetic forces. The first is the electrostatic force. When two electrons are brought close together, they repel each other. The electric charge of a particle can be either negative or positive. Electrons actually are negatively charged. Other particles (for instance, protons) have positive charges. Two particles with opposite charges attract each other, and two particles with like charges repel each other. Because of this attractive force, protons and electrons tend to group together in atoms in equal numbers, which means that atoms have no net charge. This generally cancels out the effect of the individual charges on more distant charged particles. However, you experience the electric repulsion of the electrons in a solid object whenever you touch it and your hand does not pass through it. The second kind of electromagnetic force is the magnetic force. Whenever charged particles are in motion, they generate a magnet field. The action of the magnetic force is more complex than that of the electric field, but it bears some similarities to the electric field. If you have ever played with a bar magnet, you may have noticed that it has two poles, a north pole and a south pole. If you bring together two bar magnets, the opposite poles attract and the like poles repel much like the charges in the electrostatic case. Electromagnetic forces are used extensively in our everyday lives. They are used in the electric motors in many electric appliances. They are used to drive loud-speakers

63 Electromagnetic forces are used to convert the mechanical motion produced by hydroelectric, fossil fuel burning, and nuclear power plants into electricity. Electric Circuits The operation of any electrical device requires that there be a flow of electrons, which we call an electric current. In order for electric current to continue, it must flow in a loop; otherwise, electrons will build up at some point, where they will resist the continued flow of electrons. A very simple electric circuit is pictured below. In this circuit, the battery provides frequency the power that keeps the electrons flowing around the circuit. The lines represent wires, which carry the electric current. The electric power is converted into light in the light bulb. The electrons in the light bulb filament collide with the current (I) atoms of the filament and lose some of their energy by heating up the filament. The battery converts chemical energy into electric power and that power is then converted into light energy in the light bulb. In order for the circuit to continue to work, the flow of electric current around the circuit must be maintained. If you break the loop, the current will stop flowing and the light bulb will stop glowing. Volts and Amperes Even though the circuit described above is very simple, all electric circuits work on the same principles. There must be a flow of electrons around a loop, and there must be a source of electric power, like the battery. Most electric circuits use a battery or the power provided by the electric power company through the electric outlets in the house or building. In an electric circuit there are two basic variables: current and voltage. The current is the rate of flow of electric charge, measured in units of Amperes or Amps (A). The voltage is a measure of the potential of the power supply for providing electric power. The voltage is measured in units of Volts (V). There are instruments for measuring electric current and voltage just like there are instruments (like meter sticks and scales) for measuring length and mass. Voltages are measured with voltmeters, and currents are measured with ammeters. Alternating and Direct Current

64 Batteries are designed to provide a constant voltage. For instance, a standard flashlight D cell produces a voltage of about 1.5 Volts. However, the voltage provided by a wall outlet is not constant. In fact, voltage provided by the wall outlet is oscillating at a frequency of about 60 Hz. It oscillates between a maximum of about 120 V to a minimum of about -120 V. The power company provides power in this form because less of it is lost along the power lines this way. When the voltage and current oscillate this way it is called Alternating Current (AC). When electric power comes in the form of a constant voltage and current it is called Direct Current (DC). Ohm s Law Electric circuit elements (like our light bulbs) all resist the flow of electric current. Some offer more resistance than others. The more resistance the element has, the less current will flow (at a certain voltage). Electric circuit elements can be characterized by their resistance, R, which is the ratio of the voltage applied, V, to the current through the element, I: R = V/I Some types of circuit elements have resistance which is independent of the particular value of the voltage or the current. These circuit elements are called resistors. Resistors follow Ohm s law, which states that the current through the resistor is directly proportional to the voltage. That is, a resistor s resistance is constant. Some other resistive elements do not follow Ohm s law. In other words, their resistance, (the ratio V/I), is not constant. One example of this behavior is a light bulb. As the filament in the light bulb gets hotter, it s resistance to the electric current increases. Electric Power Electric circuits convert electric power into other forms of energy including mechanical energy (motion), thermal energy, and light. The total amount of energy is conserved (never changes) so this energy must come from somewhere. This energy comes from the source of electric power, the battery or electric generating plant. The electric circuit is said to consume power. In fact, the circuit simply converts energy from one form to another. The amount of power consumed by a circuit element, P, is equal to the product of voltage applied to it, V, and the current through it, I. P = VI We measure power in units of watts. A watt is a unit of energy converted per unit time. The metric unit of energy is called a joule (J). The joule is related to the units of mass, length and time. 1 J = 1 kg m 2 /s

65 A watt is a Joule/sec. For example, a 100 watt light bulb consumes (converts to light energy) 100 joules of energy per second. If the bulb has an average of 100 V applied to it, then it has about one amp of current flowing through it on average. For a given voltage, V, the more current that flows, the more power will be consumed. Consequently, elements that have greater resistance consume less power. In fact, the power consumed by a resistor is inversely proportional to the resistance, R. P = V 2 /R Parallel and Series Circuits Most circuits consist of more than one element. A simple example of an electric circuit with more than one element is a set of Christmas tree lights. There are two basic ways that several elements can be connected. The elements can be wired in series one after another as shown below. Series Circuit There is a problem involved with wiring lights this way. If one of the lights burns out, the circuit is broken. If the circuit is broken, it no longer functions. When circuit elements are wired this way, each element add a little resistance to the total. So all the lights wired together are more resistant to current than one alone. In fact, the resistant of the whole string of lights is equal to the sum of the resistances of the individual lights. R SeriesTotal = R 1 + R 2 + +R n

66 The other way that you can combine more than one element in a circuit is in parallel. When several elements are connected in parallel, both of the leads from each element is connected by wire directly to the power supply as shown below. Parallel Circuit One advantage of connecting lights in parallel is that one lamp burning out will not interrupt the rest of the circuit. If one lamp burns out, it only breaks the current in that branch of the circuit. Current can still flow through the rest of the circuit. When several elements are connected in parallel, the amount of current being drawn from the power supply is more than would be drawn by any one of the individual elements alone. Consequently, connecting several elements together in parallel reduces the effective resistance of the entire circuit to less than any of the individual elements alone. 1 = R ParallelTotal R 1 R 2 R n

67 Your Name Lab Partner Experiment 8 Work Sheet I. Current, Voltage and Resistance You will determine the resistance of a resistor. Use the batteries as the power supply (DC). Connect the battery holder, the resistor, the voltmeter, and the ammeter as shown. A voltmeter measure the voltage across a circuit element and an ammeter measures the current flowing through the circuit element. - ammeter multimeter resistor Beginning with one battery: read the current and voltage across the resistor from your meters. Record the data in the table. Repeat with 2, 3, and 4 batteries. The current is measured in milliamps so make sure you convert to amperes (divide by 1000). Calculate the resistance of the resistor using R=V/I. # batteries Voltage (V) Current (A) Resistance (Ohms) Discussion: The resistor is ohmic, which states that the resistance is constant. Is the resistance in your table roughly constant?

68 II. Electric Generators We will explore the phenomenon of electric power using the concept of induction in the hand held mini-generator. The mini-generator works much the same way as a conventional electric generator. When you turn the hand crank it rotates a coil of wire in the magnetic field of a permanent magnet inside the generator. If there is an unbroken circuit the current will then flow out through the wire leads coming out of the generator. mini-generator wire leads light bulb This creates a complete circuit with the generator as the power supply. Current will flow from the generator into the light bulb where it will heat up the filament until it glows. Connect the light bulb to the generator as shown. Turn the crank of the generator until the light glows. If it doesn t glow at first, turn the crank faster until it does. Notice that the fast you turn the crank the brighter the lamp glows. Discussion: Why do think this happens? Now disconnect one of the wire leads and begin turning the crank as before Discussion: What happens?

69 Now connect two of the mini-generators as shown below. Turn the crank on one of the generators. Discussion: What happens to the other generator when you turn the crank on the first? How could you explain what is happening? III. Series and Parallel Circuits Look at the pictures below. Label below each picture which is a series circuit and which is a parallel circuit? Use the multimeter; set the multimeter to the 200 Ohms scale to measure the series resistors and the parallel resistors. Knowing that each resistor has a value of 50Ω. Find the theoretical total effective resistances and calculate the percent discrepancies from your experimental values