Test Prep for AP® Courses

7.1 Work: The Scientific Definition


Given Table 7.7, about how much force does the rocket engine exert on the 3.0-kg payload?

Distance Traveled with Rocket Engine Firing (m) Payload Final Velocity (m/s)
500 310
490 300
1,020 450
505 312
Table 7.7
  1. 150 N
  2. 300 N
  3. 450 N
  4. 600 N

You have a cart track, a cart, several masses, and a position-sensing pulley. Design an experiment to examine how the force exerted on the cart does work as it moves through a distance.


Look at Figure 7.11(c). You compress a spring by x, and then release it. Next you compress the spring by 2x. How much more work did you do the second time than the first?

  1. half as much
  2. the same
  3. twice as much
  4. four times as much

You have a cart track, two carts, several masses, a position-sensing pulley, and a piece of rough carpet that will fit over the track. Design an experiment to examine how the force exerted on the cart does work as the cart moves through a distance.


A crane is lifting construction materials from the ground to an elevation of 60 m. Over the first 10 m, the motor linearly increases the force it exerts from 0 to 10 kN. It exerts that constant force for the next 40 m, and then winds down to 0 N again over the last 10 m, as shown in Figure 7.49. What is the total work done on the construction materials?

The graph has meters on the x axis and newtons on the y axis. A straight line runs from the point (0, 0) to the point (10, 10). Another straight line runs from (10, 10) to (50, 10). A third straight line runs from (50, 10) to (60, 0).
Figure 7.49 A line graph displaying movement of construction materials by a crane.
  1. 500 kJ
  2. 600 kJ
  3. 300 kJ
  4. 18 MJ

7.2 Kinetic Energy and the Work-Energy Theorem


A toy car is going around a loop-the-loop. Gravity ________ the kinetic energy on the upward side of the loop, ________ the kinetic energy at the top, and ________ the kinetic energy on the downward side of the loop.

  1. increases, decreases, has no effect on
  2. decreases, has no effect on, increases
  3. increases, has no effect on, decreases
  4. decreases, increases, has no effect on

A roller coaster is set up with a track in the form of a perfect cosine. Describe and graph what happens to the kinetic energy of a cart as it goes through the first full period of the track.


If wind is blowing horizontally toward a car with an angle of 30° symbol from the direction of travel, the kinetic energy will ________. If the wind is blowing at a car at 135° symbol from the direction of travel, the kinetic energy will ________.

  1. increase, increase
  2. increase, decrease
  3. decrease, increase
  4. decrease, decrease

In what direction relative to the direction of travel can a force act on a car when traveling on level ground, and not change the kinetic energy? Can you give examples of such forces?


A 2,000-kg airplane is coming in for a landing, with a velocity 5° symbol below the horizontal and a drag force of 40 kN acting directly rearward. Kinetic energy will ________ due to the net force of ________.

  1. increase, 20 kN
  2. decrease, 40 kN
  3. increase, 45 kN
  4. decrease, 45 kN

You are participating in the Iditarod, and your sled dogs are pulling you across a frozen lake with a force of 1,200 N while a 300 N wind is blowing at you at 135° symbol from your direction of travel. What is the net force, and will your kinetic energy increase or decrease?


A model drag car is being accelerated along its track from rest by a motor with a force of 75 N, but there is a drag force of 30 N due to the track. What is the kinetic energy after 2 m of travel?

  1. 90 J
  2. 150 J
  3. 210 J
  4. 60 J

You are launching a 2-kg potato out of a potato cannon. The cannon is 1.5 m long and is aimed 30° symbol above the horizontal. It exerts a 50 N force on the potato. What is the kinetic energy of the potato as it leaves the muzzle of the potato cannon?


When the force acting on an object is parallel to the direction of the motion of the center of mass, the mechanical energy ________. When the force acting on an object is antiparallel to the direction of the center of mass, the mechanical energy ________.

  1. increases, increases
  2. increases, decreases
  3. decreases, increases
  4. decreases, decreases

Describe a system in which the main forces acting are parallel or antiparallel to the center of mass, and justify your answer.


A child is pulling two red wagons, with the second one tied to the first by a non-stretching rope. Each wagon has a mass of 10 kg. If the child exerts a force of 30 N for 5.0 m, how much has the kinetic energy of the two-wagon system changed?

  1. 300 J
  2. 150 J
  3. 75 J
  4. 60 J

A child has two red wagons, with the rear one tied to the front by a non-stretching rope. If the child pushes on the rear wagon, what happens to the kinetic energy of each of the wagons, and the two-wagon system?


Draw a graph of the force parallel to displacement exerted on a stunt motorcycle going through a loop-the-loop versus the distance traveled around the loop. Explain the net change in energy.

7.3 Gravitational Potential Energy


A 1.0 kg baseball is flying at 10 m/s. How much kinetic energy does it have? Potential energy?

  1. 10 J, 20 J
  2. 50 J, 20 J
  3. unknown, 50 J
  4. 50 J, unknown

A 2.0-kg potato has been launched out of a potato cannon at 9.0 m/s. What is the kinetic energy? If you then learn that it is 4.0 m above the ground, what is the total mechanical energy relative to the ground?

  1. 78 J, 3 J
  2. 160 J, 81 J
  3. 81 J, 160 J
  4. 81 J, 3 J

You have a 120-g yo-yo that you are swinging at 0.9 m/s. How much energy does it have? How high can it get above the lowest point of the swing without your doing any additional work, on Earth? How high could it get on the Moon, where gravity is 1/6 Earth’s?


Two objects, each with mass M, are located at x=a x=a and x=a x=a , respectively. Which of the following correctly describes the gravitational potential for a point on the x-axis located between the two objects?

  1. 2GMa x 2 a 2 2GMa x 2 a 2
  2. 2GMx x 2 a 2 2GMx x 2 a 2
  3. 2GMa x 2 a 2 2GMa x 2 a 2
  4. 2GMx x 2 a 2 2GMx x 2 a 2

An object of mass M is located at the origin, and a second object of mass M/2 M/2 is located at x=R x=R . Which of the following most closely represents the x-value in between the two objects where the gravitational potential is at a maximum?

  1. 0.5R 0.5R
  2. 0.6R 0.6R
  3. 0.7R 0.7R
  4. 0.8R 0.8R

7.4 Conservative Forces and Potential Energy


Two 4.0 kg masses are connected to each other by a spring with a force constant of 25 N/m and a rest length of 1.0 m. If the spring has been compressed to 0.80 m in length and the masses are traveling toward each other at 0.50 m/s each, what is the total energy in the system?

  1. 1.0 J
  2. 1.5 J
  3. 9.0 J
  4. 8.0 J

A spring with a force constant of 5,000 N/m and a rest length of 3.0 m is used in a catapult. When compressed to 1.0 m, it is used to launch a 50 kg rock. However, there is an error in the release mechanism, so the rock gets launched almost straight up. How high does it go, and how fast is it going when it hits the ground?


What information do you need to calculate the kinetic energy and potential energy of a spring? Potential energy due to gravity? How many objects do you need information about for each of these cases?


You are loading a toy dart gun, which has two settings; the more powerful setting compresses the spring twice as far as the lower setting. If it takes 5.0 J of work to compress the dart gun to the lower setting, how much work does it take for the higher setting?

  1. 20 J
  2. 10 J
  3. 2.5 J
  4. 40 J

Describe a system you use daily with internal potential energy.


Old-fashioned pendulum clocks are powered by masses that need to be wound back to the top of the clock about once a week to counteract energy lost due to friction and the chimes. One particular clock has three masses: 4.0 kg, 4.0 kg, and 6.0 kg. They can drop 1.3 meters. How much energy does the clock use in a week?

  1. 51 J
  2. 76 J
  3. 127 J
  4. 178 J

A water tower stores not only water, but part of the energy to move the water. How much water is in a typical tower? Make reasonable estimates for how much water is in the tower, and other quantities you need.


Old-fashioned pocket watches needed to be wound daily so they wouldn’t run down and lose time, due to the friction in the internal components. This required a large number of turns of the winding key, but not much force per turn, and it was possible to overwind and break the watch. How was the energy stored?

  1. a small mass raised a long distance
  2. a large mass raised a short distance
  3. a weak spring deformed a long way
  4. a strong spring deformed a short way

Some of the very first clocks invented in China were powered by water. Describe how you think this was done.

7.5 Nonconservative Forces


You are in a room in a basement with a smooth concrete floor (friction force equals 40 N) and a nice rug (friction force equals 55 N) that is 3 m by 4 m. However, you have to push a very heavy box from one corner of the rug to the opposite corner of the rug. Will you do more work against friction going around the floor or across the rug, and how much extra?

  1. across the rug is 275 J extra
  2. around the floor is 5 J extra
  3. across the rug is 5 J extra
  4. around the floor is 280 J extra

In the Appalachians, along the interstate, there are ramps of loose gravel for semis that have had their brakes fail to drive into to stop. Design an experiment to measure how effective this would be.

7.6 Conservation of Energy


You do 30 J of work to load a toy dart gun. However, the dart is 10 cm long and feels a frictional force of 10 N while going through the dart gun’s barrel. What is the kinetic energy of the fired dart?

  1. 30 J
  2. 29 J
  3. 28 J
  4. 27 J

When an object is lifted by a crane, it begins and ends its motion at rest. The same is true of an object pushed across a rough surface. Explain why this happens. What are the differences between these systems?


A child has two red wagons, with the rear one tied to the front by a stretchy rope or a spring. If the child pulls on the front wagon, the ________ increases.

  1. kinetic energy of the wagons
  2. potential energy stored in the spring
  3. both A and B
  4. not enough information

A child has two red wagons, with the rear one tied to the front by a stretchy rope or a spring. If the child pulls on the front wagon, the energy stored in the system increases. How do the relative amounts of potential and kinetic energy in this system change over time?


Which of the following are closed systems?

  1. Earth
  2. a car
  3. a frictionless pendulum
  4. a mass on a spring in a vacuum

Describe a real-world example of a closed system.


A 5.0-kg rock falls off of a 10 m cliff. If air resistance exerts a force of 10 N, what is the kinetic energy when the rock hits the ground?

  1. 400 J
  2. 12.6 m/s
  3. 100 J
  4. 500 J

Hydroelectricity is generated by storing water behind a dam, and then letting some of the water run through generators in the dam to turn the generators. If the system is the water, what is the environment that is doing work on it? If a dam has water 100 m deep behind it, how much energy was generated if 10,000 kg of water exited the dam at 2.0 m/s?


Before railroads were invented, goods often traveled along canals, with mules pulling barges from the bank. If a mule is exerting a 1,200 N force for 10 km, and the rope connecting the mule to the barge is at a 20° symbol angle from the direction of travel, how much work did the mule do on the barge?

  1. 12 MJ
  2. 11 MJ
  3. 4.1 MJ
  4. 6 MJ

Describe an instance today in which you did work, by the scientific definition. Then calculate how much work you did in that instance, showing your work.