AP Physics 1- Day 1 Assignment 2016

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1 AP Physics 1- Day 1 Assignment 2016 Hahnville High School Welcome to AP Physics 1! This is a college- level physics course that is fun, interesting, and challenging on a level you ve not yet experienced. It provides a wonderful opportunity to grow as a critical thinker, problem solver, and great communicator. During the next year, we will investigate relationships between various properties of objects that we call variables (because they can constantly change). It is very important that we have a tool at our disposal that will allow us to describe these relationships and to apply them to other situations; that tool is mathematics. This summer assignment, containing 6 parts, will review all of the prerequisite knowledge expected of you from Algebra, Geometry, and prior science courses. It is the quantity not the difficulty of the problems that has the potential to overwhelm, so do it over an extended period of time. By taking the time to review and understand all parts of this assignment, you will help yourself acclimate to the rigor and pacing of AP Physics 1. If you do not know how to complete a section, do not worry! This does not mean that you are not cut out for AP Physics, just that you may need to do a little more review on that topic. Below are a few websites you can visit to help review. basics It is VERY important that this assignment be completed individually. It will be a total waste of our time if you copy the assignment from a friend. This assignment is due on Tuesday, August 23, If you have any questions, you can me at tdufrene6@stcharles.k12.la.us. Good luck! 1

2 Part 1: Significant Figures, Scientific Notation, and Dimensional Analysis Significant figures, sometimes called significant digits, are key to scientific calculations. In fact, EVERY calculation you perform in AP Physics 1 must be rounded to the correct number of significant figures. Remember the rules: «All non- zero digits are significant. «Zeros are NOT significant when they re leading, or fall before a significant digit. (Ex ) «Zeros ARE significant when they re embedded, or fall between significant digits. (Ex ) «Zeros ARE significant when they re trailing, or follow a significant digit but ONLY with the presence of a decimal. (Ex ) An example of an insignificant trailing zero would be found in the number 350. Express the following the numbers in scientific notation using the appropriate number of significant figures. Keep the same unit as provided. ALL answers in physics need the appropriate unit to be correct. 1. 7,640,000 kg s m km/s Often times multiple numbers in a problem contain scientific notation and will need to be reduced by hand. Before you practice, remember the rules for exponents. When numbers are multiplied together, you the exponents and _ the bases. When numbers are divided, you the exponents and the bases. When an exponent is raised to another exponent, you the exponents and the base. Using the three rules from above, simplify the following numbers in proper scientific notation. Round to the correct number of significant figures. Remember the rules for rounding calculated answers to the correct number of significant figures: «When adding and subtracting, round to the least number of decimal places used in the calculation. «When multiplying and dividing, round to the least number of significant figures used in the calculation. 5. 3x10! 2x10! = x10! 6.0x10!! = 7. 4x10! 5x10!! = x10!! =!!!"! 9. = (!!!"! ) 10. 2x10!!! = 2

3 For the remaining scientific notation problems, be sure to use your calculator. It is important that you know how to use your calculator for scientific notation. The easiest method is to use the EE button. Ex: 7.8x10-6 would be entered as 7.8 EE - 6. Report your answers in scientific notation and to the correct numbers of significant figures x10! 8.91x10!! = x10!! 4.87x10!! = 13.!.!!!"! =!.!!!"!" x10!!! = Fill in the power and the symbol for the following unit prefixes. Look them up if necessary. These should be memorized for the upcoming year. Kilo- has been completed as an example. Prefix Power Symbol Tera Giga- Mega- Kilo k Centi- Milli- Micro- Nano- Pico- Not only is it important to know what the prefixes mean, it is also vital that you can convert between metric units. If there is no prefix in front of a unit, it is the base unit which has 10 0 for its power, or just simply 1. Remember if there is an exponent on the unit, the conversion should be raised to the same exponent as well. Convert the following numbers into the specified unit. Use scientific notation when appropriate. Remember to round to the correct number of significant figures g = kg m 2 = cm MHz = Hz mm 3 = m Gb = kb g/cm 3 = kg/m nm = m m/s = km/hr 3

4 Solve the following unit conversions using dimensional analysis; show all your work for full credit. Round your answers to the appropriate number of significant figures. 23. How many meters are in feet? 24. American football uses a field that is yd long, whereas a soccer field is m long. Which field is longer, and by how much? Give yards, meters, and percent. 25. A light- year is the distance light travels in one year (at speed = x 10 8 m/s). (a) How many meters are there in 1.00 light- year? (b) An astronomical unit (AU) is the average distance from the Sun to Earth, 1.50 x 10 8 km. How many AU are there in 1.00 light- year? 26. If there are 745 Watts for every unit of horsepower, how many horses would it take to power a single hundred- watt light bulb? 27. If a woodchuck can chuck 2 cubic meters of wood per minute, how many cubic centimeters per second is that equivalent to? 28. A typical atom has a diameter of about 1.0 x m. (a) What is this in inches? (b) Approximately how many atoms are along a 1.0 cm line, assuming they just touch? 29. Calculate the number of seconds you ve been alive. Try to be as precise as possible! Figure out how many days it s been since your last birthday how many hours at what time were you even born??? Make note your birthday along with the date and time that you complete the problem. 30. The AIDS virus is 0.06 nm in length. How many inches is this? 31. Calories are used to express energy quantities. If 1 calorie = joules, how many calories would be equivalent to joules? 32. A dietary calorie (often represented as Calorie) is actually a kilocalorie. (1 dietary Calorie = 1000 calories) How many dietary calories would be described by the previous problem? 4

5 Part 2: Geometry Calculate the area of the following shapes. It may be necessary to break up the figure into common shapes. 1. Area = 2. Area = Calculate the unknown angle values for questions θ = 16! φ = 5

6 4. Lines m and n are parallel. A = 75 o B = C = D = E = F = G = H = θ! = 5. θ! = θ! = θ! = θ! = A = 6. B = C= D = 6

7 Part 3: Trigonometry Write the formulas for each one of the following trigonometric functions. Remember SOHCAHTOA! sinθ = cosθ = tanθ = Calculate the following unknowns using trigonometry. Use a calculator, but show all of your work. Please include appropriate units with all answers and round to 3 significant figures. (Watch the unit prefixes!) 1. y = x = 5. R = θ = 2. d! = d! = 6. d = θ = 3. x = y = 7. y = θ = 4. c = θ = 8. x = d = 7

You will need to be familiar with trigonometric values for a few common angles. Memorizing this diagram in degrees or the chart below will be very beneficial for next year.

8 You will need to be familiar with trigonometric values for a few common angles. Memorizing this diagram in degrees or the chart below will be very beneficial for next year. How the diagram works is the cosine of the angle is the x- coordinate and the sine of the angle is the y- coordinate for the ordered pair. Write the ordered pair (in fraction form) for each of the angles shown in the table below. θ cosθ sinθ 0 o 30 o 45 o 60 o 90 o Refer to your completed chart above to answer the following questions. 9. At what angle is sine at a maximum? 10. At what angle is sine at a minimum? 11. At what angle is cosine at a minimum? 12. At what angle is cosine at a maximum? 13. At what angle is the sine and cosine equivalent? 14. As the angle increases in the first quadrant, what happens to the cosine of the angle? 15. As the angle increases in the first quadrant, what happens to the sine of the angle? Use the figure below to answer the following problems. 16. Find an expression for h in terms of l and θ. 17. What is the value of h if l = 6 m and θ = 40? 8

9 Part 4: Manipulating Equations Section I: Solve the equations for the variable indicated. Show all your steps. 1) 5) 2) 6) 3) 7) 4) 8) Section II: Evaluate the following using the information given. Round to the correct number of significant figures. 9) 12) 10) 13) 11) 14) 9

10 Section III: Solve the following using the equations at the right. Round to the correct number of significant figures. 15) Using the first equation, solve for t given that v 0 = 5 m/s, v f = 25 m/s, and a = 10 m/s 2. v! = v! + at x! = x! + v! t +!! at! v!! = v!! + 2a(x! x! ) 16) a = 10 m/s 2, x 0 = 0 m, x f = 120 m, and v 0 = 20 m/s. Use the second equation to find t. 17) How does each equation simplify when a = 0 m/s 2 and x 0 = 0 m? Section IV: Solve the following using the equations at the right. Round to the correct number of significant figures. 18) If ΣF = 10 N and a = 1 m/s 2, find m using the first equation. 19) Given ΣF = f!, m = 250 kg, μ! = 0.2, and N = 10m, find a. ΣF = ma f! = μ! N f! μ! N F! = kx 20) Given the following values, determine if the third equation is valid. ΣF = f!, m = 90 kg, and a = 2 m/s 2. Also μ! = 0.1, and N = 5 N. 21) Use the first equation in Section III, the first equation in Section IV, and the givens below to find ΣF. m = 12 kg, v! = 15 m/s, v! = 5 m/s, and t = 12 s. 22) Use the last equation to solve for F s if k = 900. N/m and x = m. Section V: Solve the following using the equations at the right. Round to the correct number of significant figures. 23) Given that v is 5 m/s and r is 2 meters, find a. a =!!! τ = rfsinθ 24) Originally, a = 12 m/s 2, then r is doubled. Find the new value for a. 25) Use the second equation to find θ when τ = 4.0 Nm, r = 2.0 m, and F = 10.0 N. 10

11 Section VI: Solve the following using the equations at the right. Round to the correct number of significant figures. 26) Use the first equation to solve for K if m = 12 kg and v = 2.0 m/s. 27) If U g = 10. J, m = 10. kg, and g = 9.8 m/s 2, find h using the second equation. K =!! mv! ΔU! = mgh W = F(Δx)cosθ U! =!! kx! 28) The third equation can be used to find W if you know that F is 10. N, x is 12 m, and θ is 180. P =!! P = Fv!"# cosθ 29) Use the value for W you found in the previous question to find P if t = 2 s. Which equation do you need for this? 30) Given U s = 12 joules, and x = 0.5 m, find k using the fourth equation. 31) For the same value of x as given in the previous problem and the k value you just found, use the last equation in Section IV to find F s. 32) For P = 2100 W, F = 30 N, and θ = 0, find v!"# using the last equation in this section. Section VII: Solve the following using the equations at the right. Round to the correct number of significant figures. 33) p is 12 kgm/s and m is 25 kg. Find v using the first equation. p = mv FΔt = Δp Δp = mδv 34) In calculations,, or delta, means final state minus initial state. So, v means v f v i and p means p f p i. Find v f using the third equation if p f = 50 kgm/s, m = 12 kg, and v i and p i are both zero. 35) Use the second and third equation together to find v i if v f = 0 m/s, m = 95 kg, F = N, and t = 0.20 s. 11

Section VIII: Solve the following using the equations at the right. Round to the correct number of significant figures. 36) T p is 1.00 second and g is 9.8 m/s 2. Find l using the second equation. T! = 2π!

12 Section VIII: Solve the following using the equations at the right. Round to the correct number of significant figures. 36) T p is 1.00 second and g is 9.8 m/s 2. Find l using the second equation. T! = 2π!!! 37) m = 8.00 kg and T s = 0.75 s. Solve for k. 38) Given that T p = T, g = 9.8 m/s 2, and that l = 2 m, find f (the units for f are Hertz). T! = 2π!!! T =!! F! =!"#!! U! =!"#! 39) Find F g if G = m 3 kg - 1 s - 2, M = kg, m = 1200 kg, and r = 2000 m. 40) What is r if U g = J, G = m 3 kg - 1 s - 2, M = kg, and m = 1200 kg? 12

13 Part 5: Graphing OVERVIEW Since the late 1990 s, the AP Physics exam has placed an increased emphasis on physics laboratory experience, interpreting laboratory investigations, and interpreting graphs that accompany a laboratory experience. Questions every year appear on the exam, usually centering on a laboratory experience like determining gravity or making sense of data on a position v. time graph. Occasionally, an AP exam has included a question asking students to create or devise an experiment that incorporates certain equipment. Those students serious about earning a passing score will work to understand the meaning of the graphs obtained in lab and correctly answer all post- lab questions. In this review, we are going to look at graphical interpretation. GRAPHING DATA CORRECTLY The goal of a physics experiment is to determine how two sets of measurements are related to each other. In some physics experiments, you do not have clearly defined independent and dependent variables. Instead, your focus is in understanding the two things you are measuring and why you need to measure them. Once you have two sets of measurements, your next step is to create the graph. NEVER free- hand sketch a graph. NEVER use data table points to determine a slope (best fit line only). Use either graph paper or graphing software. Use the x- axis for the independent variable (that which is experimentally varied; also known as the manipulated variable) and the y- axis for the dependent variable (that which is a function of the independent variable; also known as the responding variable). For example, if your graph is position vs. time, position is on the y- axis and time is on the x- axis. You are attempting to see how the position varies with time, or stated in another way, you are studying time dependent position. You should always use a straight- edge if possible. Also, always label the axes and include units. A GENERAL APPROACH TO LINEAR GRAPHING Let s say we need to determine the spring constant, or the measure of the stiffness/strength of the spring, for a linear spring. To find the spring constant, we need to set up an experiment with a spring loaded with various masses. The spring stretches different amounts when we add different sized masses. During this experiment, we measure two quantities, the weight (force) in newtons hanging on the spring and the stretch of the spring in meters. For a visual of the experimental design, click here. A table of results is below. Graph the data. Problem 1 Force (N) Stretch (m) SLOPE y x = EQUATION = 13

This is a typical graph of a physics experiment. The data should clearly show a relationship between the two sets of measurements. In this case, it is a linear relationship.

14 This is a typical graph of a physics experiment. The data should clearly show a relationship between the two sets of measurements. In this case, it is a linear relationship. The line is a trend line or line of best fit or best- fit line. All data does not fall on the line, but that is to be expected when dealing with real data. However, your best- fit- line should always include equal numbers of points above and below the line. Also, consider if the point (0, 0) has physical meaning. For our example, ask yourself, Would the spring stretch at all if zero mass was hanging? The answer is no. Therefore, the trend line should pass through (0, 0). The answer to other experiments may not always be yes, and that s when your trend line doesn t have to pass through the origin. The equation for the spring is the equation of the graph s trend line. This simply follows the form y = mx + b or for our example, F = mx + b. We will get into the specifics of this in the fall, but for now, determine the slope (with units) and write the equation for this data (omit the y- intercept, b.) Remember that the equation of the line tells us the relationship between the variables in play. Since our equation is y = m(x), where m is your slope, we know that a linear relationship exists. WHAT IF THE GRAPH IS CURVED? Here is where the fun begins. If we get a nonlinear relationship (a curved graph) between our physical quantities, we will need to investigate further to figure out the exact model for this relationship. This is the most important data analysis skill you can learn in an AP Physics course. You will be practicing it by working with graphs that present you with interesting relationships. The following are the most common relationships: Relationship Function Slope Intercept Form Sketch of Graph Linear f(x) = x y = mx Reciprocal f(x) =!! y =!! Quadratic f(x) = x 2 y = mx 2 Inverse f(x) =!!! y =!!! Radical (or Square Root) f(x) = x y = m x 14

15 LINEARIZING or MANIPULATING DATA The process of linearizing data is useful because it makes it much easier to plot and helps you to know whether the data fits the law you re testing for. With linearized data, it s much easier to apply statistics, to calculate accurate values for the slope and intercept, and to get a value for the coefficient of correlation, which tells you how well the data fits the trend line. You can also calculate the uncertainties in the slope and intercept. It is a simple five- step process: 1. Graph the original data. 2. Determine the type of relationship you determined your graph represents based on its shape (quadratic, reciprocal, square root, etc.). 3. Manipulate your data s x values according to this relationship. For example, if the relationship is quadratic, x changes to x 2 so square all your x values. If the graphed shape would have been a square root curve, you d take the square root of all your x values. 4. Create a graph of the new data. 5. Use the slope- intercept form of the new best- fit line to create the exact relationship for your data. (Can you can see why this process is called linearizing the data?) PROBLEM 2 Here is a sample set of data that represents an object s position as a function of time, or position vs. time. Graph the data. Then create a second graph to linearize the data by manipulating time. Enter this manipulated data into the empty table column. For the linear graph, determine the slope (with units) and the equation for the linear plot. Position (m) Time (s) RELATIONSHIP SLOPE EQUATION = = = 15

PROBLEM 3 We are considering an experiment in which we put a series of masses on a spring and then set the spring/mass system into motion. The resulting motion is simple harmonic motion (SHM).

16 PROBLEM 3 We are considering an experiment in which we put a series of masses on a spring and then set the spring/mass system into motion. The resulting motion is simple harmonic motion (SHM). We measure each mass we place on the spring and the period of the SHM. The period is always constant for any one mass. Here is a set of data that was gathered. Graph the data of Period vs. Mass. Then, linearize the data to determine the proper relationship. Fill in the data table. Plot Period vs. Manipulated Mass and Manipulated Period vs. Mass. Both plots should be linear. Determine the slope (with units) and equation for each linear graph. Mass (kg) Period (s) RELATIONSHIP = SLOPE = EQUATION = RELATIONSHIP = Do your slopes match? Should they? Explain your reasoning in complete sentences. SLOPE EQUATION = = 16

17 Graph the following sets of data using proper graphing techniques addressed in the previous section. The first column refers to the y- axis and the second column to the x- axis. PROBLEM 4 Plot a graph for the following data recorded for an object falling from rest: Velocity (ft/s) Time (s) a. Slope = b. Equation = c. What is the relationship between the variables? d. What do you expect the velocity to be after 4.5 seconds? e. How much time is required for the object to attain a speed of 100 ft/s? PROBLEM 5 Plot a graph showing the relationship between frequency and wavelength of electromagnetic waves: Frequency (Hz) Wavelength (m)

18 a. Slope = b. Equation = c. What is the relationship between the variables? d. What is the wavelength of an electromagnetic wave of frequency 350 Hz? e. What is the frequency of an electromagnetic wave of wavelength 375 m? 18

19 Part 6: Conceptual Preview & Free Response Practice Questions for you to think about and then research Do your best to answer the following questions after examining the provided videos and links. These concepts are important ideas we will discuss throughout the year. Your responses should be handwritten and follow the AP Physics Paragraph- Length Response document from the College Board; it can be found at the address below: media.collegeboard.org/digitalservices/pdf/ap/paragraph- length- response.pdf 1. Kinematics: A gun is fired parallel to the ground. At the same instant, a bullet of equal size and mass next to the muzzle is released and drops to the ground. Which hits the ground first and why? motion 2. Newton s Laws: Why can you exert a greater force on the pedals of a bicycle if you pull up on the handlebars? manley- newton- s- 3- laws- with- a- bicycle forces- and- motion 3. Work and Energy: Consider a fly that is hovering on the inside of your car as you are traveling down the Interstate. Does it have more or less kinetic energy than the car? does- work- work- peter- bohacek skate- park 4. Momentum and Impulse: Describe why a watermelon will be obliterated when you drop it in a parking lot but will remain intact when dropped from the same height into a pool. lab 5. Circular Motion and Gravitation: Either for fun or for physics (sometimes you can t tell these apart ) you are swinging a rock attached to a string over your head. Suddenly the string breaks. Describe the new motion of the rock. Support your answer with a diagram. act 6. Waves and Sound: If you blow across the top of a Coke bottle, a specific note is produced. Add a little water to the bottle and the pitch changes. Add more water and it changes even more why? on- a- string 7. Electricity: Why can birds sit on high powered electrical wires and not be electrocuted? vocabulary hockey 19

AP Physics C Summer Assignment

AP Physics C Summer Assignment Welcome to AP Physics C! It is a college level physics course that is fun, interesting and challenging on a level you ve not yet experienced. This summer assignment will