AP Physics 1 Workbook, Exercises of Physics

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AP

®

Physics 1

Workbook | 2019

| ii

Contents

2 About This Workbook

3 Unit 1: Kinematics

29 Unit 2: Dynamics

61 Unit 3: Circular Motion and Gravitation

89 Unit 4: Work and Energy

127 Unit 5: Momentum

165 Unit 6: Simple Harmonic Motion

193 Unit 7: Torque and Rotation

225 Unit 8: Electric Charge and Electric Force

251 Unit 9: DC Circuits

281 Unit 10: Mechanical Waves and Sound

315 Unit 11: Review Questions

347 Appendix

348 AP Physics 1 Equation Sheet

350 AP Physics 1 Science Practices

351 AP Physics 1 Task Verbs used in Free-Response Questions

352 Graphical Methods Summary

353 Writing Tips

About This Workbook

Background The AP Physics 1 course is designed to promote student learning of essential physics content and foster the development of deep conceptual understanding. The instructional approaches utilized in this workbook are informed by research on student learning and knowledge construction, especially with regard to physics principles.

Contents This workbook is a compilation of problems written by high school and higher education physics faculty to help students and teachers prepare for the AP Physics 1 Exam. The AP Physics 1 Exam requires students to be able to think about physics both conceptually and mathematically as well as to write about physics. Thinking about physics and defending claims with writing may be new and challenging for students, and this workbook provides helpful guidance in supporting students’ development of this skill.

Unit 1 -

Kinematics

Workbook | 2019

UNIT 1 NAME DATE

Scenario Angela is running at 3 m/s toward the bus 15 m away.

Using Representations PART A: Below is a table of Angela’s position at each second. Complete the table. Then, on the diagram of Angela and the bus, create a motion map of Angela’s position at every second. Do this by marking with a dot where Angela is at every second.

X Time (s) 0 1 2 3 4 5 Y Position (m) 0 3 6

PART B: Another way to represent Angela’s motion is by creating a position vs. time graph. Finish filling out the data table above and then mark Angela’s position at every second on the graph. (Plot the data points with solid filled-in dots.) Sketch a best-fit line through the data points by drawing a single continuous straight line through the points. (Sketch the best-fit line as close as possible to all points and as many points above the line as below.)

Quantitative Analysis PART C: Calculate the slope of the line you drew in Part B by choosing two points on the line and filling in the equation below. (Choose two locations on the line that will be used to calculate the slope. Circle these two places on the line—remember DO NOT use data points from the table.)

slope rise

run

y y

x x

 ^ ^  ^    

2 1 2 1

m m

s s

m

  s

   

The slope of a position vs. time graph represents the (^) physical quantity. (Hint: Check units!)

Using the equation for a line ( y  mx  b ), write an equation (including units) for the position vs.

time line given above. (Remember that m is the slope and b is the vertical intercept.)

letter =^ number letter +^ number Write a more general equation for Angela’s motion using standard physics symbols (x, v, t).

letter =^ letter letter

Kinematics (^) | 1.B Position and Velocity

UNIT 1 NAME DATE

Scenario A toy company claims to have developed two toy car models which they call A and B, where the

average speed of each car is identical ( 0 50.  0 02. ms ). Each group of students is given two toy cars

(one of each model), metersticks, and stopwatches and is asked to test the toy company’s claim.

Experimental Design PART A: The students decide that they need to collect distance and time data for each car to test the company’s claim. The students design a procedure. Cross out any extraneous steps and order the remaining procedural steps: Turn the car on and release along the measured path. Gather equipment. Repeat to reduce error. Measure and record the time the car took to travel the 2 meters with a stopwatch. Measure a 2-meter-long path on the floor. Draw a data table in your notebook. Data Analysis PART B: Given is a data set collected by students in the class. Based on these data, what conclusion should the students make about the hypothesis that the two cars, A and B, have the same speed? The cars have the same average speed. The cars have different average speeds. Explain your choice in one short sentence.

Experimental Design PART C: The students decide that additionally they want to test the toy company’s claim that the car’s speed is constant throughout the motion. How, if at all, does the experimental procedure from Part A need to be modified to verify that the car’s instantaneous speed is constant? Angela thinks they should use a motion sensor to collect speed vs. time data. If the graph of speed vs. time is horizontal with a zero slope, the instantaneous speed is constant. Blake thinks that they should use photogates positioned at the beginning and end of the 2-meter-long track to determine the instantaneous speed of the cart. The students measure the length of the cart and divide this length by the time recorded by the photogate to determine the instantaneous speed. Identify which student’s procedure will provide evidence for the claim that the instantaneous speed of the cart is constant.

Lab Group Number

CAR A

Speed

CAR B

Speed 1 0.45 m/s 0.54 m/s 2 0.46 m/s 0.52 m/s 3 0.42 m/s 0.56 m/s 4 0.43 m/s 0.55 m/s 5 0.74 m/s 0.23 m/s 6 0.44 m/s 0.54 m/s AVERAGE 0.49 m/s 0.49 m/s

Kinematics (^) | 1.C Average vs. Instantaneous Speed

1.D Velocity Is a Vector!

Using Representations PART D: Based on the slopes you calculated in Parts B and C, sketch a velocity vs. time graph for Angela and Blake. Make each graph a different color and include a key.

Argumentation PART E: Carlos makes the following claim about the intersection point of the two lines on the position vs. time graph in Part A. “The point on the position vs. time graph where the two lines cross represents the time when Angela and Blake are at the same position and traveling at the same velocity.” The student’s claim is partially correct. Fill in the blanks of the following statement using evidence from the graph to correct the student’s claim.

Claim: I agree that the physical quantity is the same because Angela and Blake do have the same

physical quantity of^ number meters at^ number seconds. However, I do not agree that they have the same (^) physical quantity because the slope of one line is (^) number m/s and the slope of the other line

is (^) number m/s.

UNIT 1 NAME DATE

Kinematics (^) | 1.E Relative Velocity

Scenario Blake and Carlos are playing on a train while Angela watches. While the train passes Angela, it is traveling at 5 m/s to the east. At this time, Blake is running at 2 m/s east relative to the train toward Carlos (who is taking a break). (All speeds given for Blake are relative to the train.)

Using Representations PART A: Identify and label a direction to be positive. In the sketch above, label the positive direction. Sketch a motion map based on Angela’s measurement of Blake’s motion.

Sketch a motion map based on Carlos’s measurement of Blake’s motion.

Data Analysis PART B: Use the diagram in Part A to determine Blake’s speed relative to Angela.

PART C: Blake now turns around and runs at 2 m/s west. Use the diagram at right to determine Blake’s velocity relative to Angela’s.

UNIT 1 NAME DATE

Kinematics (^) | 1.F Constant Velocity

Scenario Carlos places a constant motion vehicle on the ground and releases it so that the vehicle travels down the hall at 5 m/s in a straight line for 10 seconds.

Using Representations PART A: Scale and label the axes on the graph to the right. Draw a velocity vs. time graph of the constant motion vehicle for the first 10 seconds of its motion.

Argumentation PART B: Collect evidence about the physical meaning of the slope of the graph that could be used to support a claim. Fill in the blanks below.

Evidence: The slope of the velocity vs. time graph

is equal to (^) number units. (^) units is also the unit for (^) physical quantity.

PART C: Claim: The constant motion vehicle will travel a distance of 50 meters during the 10-second time

interval. Collect evidence about the physical meaning of the area under the line on the graph that can be used to support the claim above. Using the equation for the area of a rectangle ( Area = length × width ), write an equation (including units) for the area of the rectangle between the velocity vs. time line and the x-axis between t = 0 and t = 10 seconds. Evidence: The area under the line of the velocity vs. time graph is equal to (^) number units × (^) number

units =^ number units. This area is also known as the^ physical quantity of the vehicle.

Reasoning: Fill in the blanks of the following statement.

The claim makes sense because if the constant motion vehicle is traveling at a velocity of

number m/s, then each second it will move a distance of^ number meters. After 2 seconds, the vehicle has moved (^) number meters. After 3 seconds, it has moved (^) number meters. After

number seconds, it has moved 25 meters. Quantitative Analysis PART D: Rewrite the equation for the area of a rectangle ( Area = length × width ) using the symbols and numbers (with units) from the graph in Part A between t = 0 and t = 10 seconds.

letter =^ number (with units) letter The area under a velocity vs. time graph represents the (^) physical quantity. (Hint: Use the units.)

UNIT 1 NAME DATE

Kinematics (^) | 1.G Graphs of Velocity

Scenario A car traveling in a straight line to the right starts from rest at time t = 0_. At time_ t = 2 s , the car is traveling at 4 m/s_. At_ t = 4 s the car is traveling at 8 m/s_._

Using Representations PART A: Scale and label the axes on the graph to the right. Using the data table below, plot a velocity vs. time graph for the car for the first 4 seconds it is traveling. Time (s) Speed (m/s)

0 0 1 2

2 4 3 6 4 8

Argumentation

PART B: Evidence: Calculate the slope of the velocity vs. time graph in Part A using two points on the line

(NOT data points).

slope rise run

y y x x

   

 ^ ^      

2 1 2 1 s

ms ms s

m   s 2

   

Claim: Use the evidence above to make a claim by filling in the following blanks:

The slope of the velocity vs. time graph is equal to (^) number unit. (^) unit is also the unit for physical quantity. Quantitative Analysis Area  12 bh

PART C: Rewrite the equation for the area of a triangle ( Letter Area =^ ^12 Number(with units) Number(with units) base × height ) using the symbols and numbers (with units) from the graph in Part A between t = 0 and t = 4 seconds.

Letter^ letter^ =^ ^ Number(with units) Number(with units)

2 number (with units)^ number (with units)

Write a more general equation for the car using standard physics symbols (x , vf , and t).

Letter^ letter^ =^ ^ Number(with units) Number(with units)

2 letter^ letter

The area under a velocity vs. time graph represents the (^) physical quantity. (Hint: Check units!)

1.H Relationships Between Position, Velocity, and Acceleration

Using Representations PART C: Use the graph in Part A to draw an acceleration vs. time graph for the motion represented above.

PART D: Use the graph in Part A to draw a position vs. time graph for the motion represented above. The position vs. time graph will pass through the two dots plotted for you.

UNIT 1 NAME DATE

Kinematics (^) | 1.I The Chase

Scenario A truck is traveling at a constant speed of 20 m/s through a school zone. At time t = 0 seconds, he passes a hidden police car that is at rest. Five seconds after the truck passes, the police car begins accelerating at a constant rate of 2 m/s^2 in order to catch the truck.

Using Representations PART A: On the axis at right, sketch and label graphs of the velocity of the truck and the police car as functions of time for the first 40 seconds after the truck passes the hidden police car. Use different colors or different lines (e.g., dashed vs. solid) to differentiate between the truck and the police car. Include a key.

Data Analysis PART B:

i. Using the graph you made in Part A, determine the time at which the speed of the truck is equal to the speed of the police car. Mark this time as t 1. ii. How will the positions of the police car and the truck compare when they have the same speed and why?

PART C: Explain in a short sentence or two how you could use the graph you made in Part A to determine the time at which the truck and the police car are in the same location.

UNIT 1 NAME DATE

Kinematics (^) | 1.J Vertical Motion

Scenario A rocket fires its engines to launch straight up from rest with an upward acceleration of 5 m/s^2 for 10 seconds. After this time, the engine shuts off, and the rocket freely falls straight down back to Earth’s surface.

Using Representations PART A: Sketch a graph of the acceleration as a function of time from t = 0 seconds to t = 10 seconds.

PART B: Sketch a graph of the velocity as a function of time from t = 0 seconds to t = 10 seconds.

Data Analysis PART C: From the graph drawn in Part B, determine the velocity of the rocket after the initial 10 seconds of travel.

The velocity of the rocket at the end of 10 seconds is. PART D: From the graph drawn in Part B, determine the height of the rocket after 10 seconds.

Height =

Argumentation PART E: Make a claim about the numerical value of the acceleration of the rocket 10.1 seconds after firing when the rocket engines have been completely shut off. (Fill in the blanks.) The acceleration of the rocket 10.1 seconds after it was launched is.

1.J Vertical Motion

Use the definition of free fall to explain your reasoning for your claim in Part E.

PART F: 10.1 seconds after the rocket was launched, indicate whether the rocket moving upward or downward.

Upward Downward Choose one piece of evidence to support your claim and write it below.