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AP Physics C: Mech

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Unit 3

3.5 MC Answers and Review

9 min read•december 30, 2021

AP Physics C: Mechanics ⚙️

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Answers and Review for Multiple Choice Practice on Work, Energy, and Power

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⛔STOP⛔ Before you look at the answers make sure you gave this practice quiz a try so you can assess your understanding of the concepts covered in Unit 3. Click here for the practice questions: AP Physics C: Mechanics Multiple Choice Questions. Facts about the test: The AP Physics C: Mechanics exam has 35 multiple choice questions and you will be given 45 minutes to complete the section. That means it should take you around 15 minutes to complete 12 questions.

The following questions were not written by College Board and, although they cover information outlined in the AP Physics C: Mechanics Course and Exam Description, the formatting on the exam may be different.

1. A 0.5kg object moves along a path according to the potential energy function U(x) = 0.25x^3, where U is in Joules and x is in meters. If the total energy of the particle is 14 J, find its speed at x = 2m.

A. 2.0 m/s

B. 6.9 m/s

C. 12 m/s

D. 48 m/s

Answer: First, find the total potential energy at x = 2m by plugging 2 in for x in the potential energy function. The potential energy of the object is 2 J at x = 2 m. Since the rest of the mechanical energy must be kinetic energy, plug 12 J into K = 1/2mv^2 and solve for v.

📄 Study AP Physics C: Mechanics, Unit 3.2: Forces and Potential Energy

2. A feather and a bowling ball are dropped from the top of a cliff. Assuming no air resistance, which of the following statements are true?

A. The bowling ball will reach the ground before the feather.

B. When they reach the ground, the bowling ball is going faster than the feather.

C. When they reach the ground, the bowling ball has more kinetic energy than the feather.

D. Just as they were released, both objects had the same about of gravitational potential energy.

Answer: Since there is no air resistance, the only force acting on both objects is gravity, so they will accelerate at the same rate. This means that they will have the same speed throughout the fall and reach the ground at the same time. Since the bowling ball is more massive, it will have more energy - both gravitational potential energy at the top of the cliff and kinetic energy as it reaches the ground.

📄 Study AP Physics C: Mechanics, Unit 3.2: Forces and Potential Energy

3. An object’s potential energy function is given by U(x) = 7x^2 + 4. Which of the following is an expression for the force on the particle?

A. F(x) = -(7/3)x^3 + 2x

B. F(x) = -14x

C. F(x) = (7/3)x^3 + 2x

D. F(x) = 14x

Answer: We can find the force by taking the negative derivative of the potential energy function. If you take the derivative of 7x^2 + 4, you get 14x. Then, make it negative.

📄 Study AP Physics C: Mechanics, Unit 3.2: Forces and Potential Energy

4. A librarian pushes a 100kg cart of books up a ramp at a constant speed of 1.5 m/s. It takes him 5 seconds to get to the top of the ramp, which has a height of 6.5 meters. With how much force is he pushing?

A. 850 N

B. 1275 N

C. 1911 N

D. 6370 N

Answer: First, find the power output of the librarian by finding the change in potential energy divided by time. The total power output is 1274 W, and then use the constant speed to find the force.

📄 Study AP Physics C: Mechanics, Unit 3.4: Power

5. Two identical rocks are launched vertically upward with a slingshot. If Rock A is launched with twice the speed as Rock B, which of the following statements are true? Assume negligible air resistance.

A. The maximum height of Rock A will be equal to the maximum height of Rock B.

B. The maximum height of Rock A will be twice as large as the maximum height of Rock B.

C. The maximum height of Rock A will be four times as large as the maximum height of Rock B.

D. The maximum height of Rock A will be eight times as large as the maximum height of Rock B.

Answer: If Rock A is launched with twice the speed, it starts with four times the kinetic energy, since K = 1/2mv^2. Energy is conserved, so at maximum height, Rock A will have four times the gravitational potential energy as Rock B. Since gravitational potential energy is directly proportional to the height of the rocks (and the rocks are identical, so they have the same mass), Rock A's maximum height will be four times as large as Rock B's.

📄 Study AP Physics C: Mechanics, Unit 3.1: Work, Energy, and Power and Work-Energy Theorem

6. A cart sits at rest at the top of a hill with a height of 25 meters. Assuming no friction, how fast is it going when it gets to the bottom of the hill?

A. 22 m/s

B. 25 m/s

C. 490 m/s

D. Impossible to know without knowing the mass of the cart.

Answer: This is a conservation of energy question. Set the potential energy expression at the top of the hill equal to the kinetic energy expression at the bottom of the hill. The mass on each side of the equation cancels, and therefore, solve for v.

📄 Study AP Physics C: Mechanics, Unit 3.3: Conservation of Energy

7. A 1010 kg sports car is moving at a speed of 45 m/s on a straight road. A 1300 kg sedan is moving at a speed of 26 m/s on the same road. Both encounter the same constant braking force and are brought rest. Which car travels a shorter distance before stopping?

A. Impossible to know with the information given.

B. Both travel the same distance

C. The sports car

D. The sedan

Answer: This is a Work-Energy Theorem question. First, find the initial kinetic energy of each car. If both cars stop, their final kinetic energy is zero. Remember that Change in Energy = Work = Force x distance x cos(theta). If both are stopped by the same constant force, whichever one has the smaller kinetic energy will travel a shorter distance to stop.

📄 Study AP Physics C: Mechanics, Unit 3.1: Work, Energy, and Power and Work-Energy Theorem

8. A crane delivers 200kW of power as it lifts a cargo container 33 meters to the 10th floor of a new building. It takes the crane 15 seconds to lift the container at a constant speed. What is the mass of the cargo container?

A. 90 kg

B. 400 kg

C. 900 kg

D. 9000 kg

Answer: Remember to convert 200kW to Watts. Then, use the power equation P = dE / dt to find dE. Since the crane is lifting at constant speed, the only energy change is in potential energy. Use the potential energy equation to solve for mass.

📄 Study AP Physics C: Mechanics, Unit 3.4: Power

9. A 4.0 kg cart sits at rest at the top of a 20 meter frictionless hill. After it rolls down the hill, it encounters a massless, frictionless spring, which it compresses 0.5 meters and comes to rest again. What is the spring constant of the spring?

A. 784 N/m

B. 1568 N/m

C. 3136 N/m

D. 6272 N/m

Answer: This is a conservation of energy question. First, find the potential energy at the top of the hill, and then set it equal to the spring potential energy equation. Solve for k.

📄 Study AP Physics C: Mechanics, Unit 3.3: Conservation of Energy

10. A spring is stretched 4 meters from its equilibrium position by a conservative force F, measured in Newtons. If the expression for the spring force is F(x) = -3x^2, what is the resulting change in potential energy?

A. 6 J

B. 12 J

C. 64 J

D. 192 J

Answer: To find the potential energy function, integrate the force function and multiply it by -1. Then, plug 4 meters into the potential energy function to find the change in potential energy of 64 Joules.

📄 Study AP Physics C: Mechanics, Unit 3.2: Forces and Potential Energy

11. A babysitter pulls the handle of a wagon with a force F at an angle theta with the ground. The work done by F as it the wagon moves a distance D across the ground can be expressed using which of the following?

A. FD

B. FDcos(theta)

C. FDsin(theta)

D. FDtan(theta)

Answer: This is the definition of work. Work is calculated by multiplying the force vector by the distance traveled. As the F is at an angle, you need to take the force component that is in the same direction as the distance. This is Fcos(theta).

📄 Study AP Physics C: Mechanics, Unit 3.1: Work, Energy, and Power and Work-Energy Theorem

12. The potential energy function of a 2.0kg object moving along an x-axis is expressed U(x) = x^2. What is the acceleration of the particle at x = 5.0m?

A. -10 m/s^2

B. -5 m/s^2

C. 12.5 m/s^2

D. 25 m/s^2

Answer: Use the relationship between potential energy and force, as well as Newton's 2nd Law, for this question. First, take the negative derivative of U(x) to find F(x) = -2x. Then, plug F(x) into F=ma to find the acceleration.

📄 Study AP Physics C: Mechanics, Unit 3.2: Forces and Potential Energy

13. A arrow is shot straight upward into the air. Compare the work done by gravity as the arrow travels upward versus when it is on the way down.

A. The work done by gravity is positive in both directions.

B. The work done by gravity is positive on the way up and negative on the way down.

C. The work done by gravity is negative on the way up and positive on the way down.

D. The work done by gravity is negative in both directions.

Answer: The force of gravity always acts downward. As the arrow goes upward, F and d are in opposite directions, so the work is negative. On the way down, F and d are in the same direction, so the work is positive.

📄 Study AP Physics C: Mechanics, Unit 3.2: Forces and Potential Energy

14. Two identical masses start with a speed of 5 m/s and travel up a frictionless ramp until they stop. If Ramp A is tilted at a 30 degree angle, and Ramp B is at a 60 degree angle, which mass is higher from the ground on their respective ramps?

A. The masses travel to the same height above the ground.

B. The mass on Ramp A is higher from the ground.

C. The mass on Ramp B is higher from the ground.

D. There is not enough information to tell.

Answer: This is a conservation of energy question. If there is no friction on the ramp, there is no energy loss in either mass. Therefore, if they start with the same mass and same speed, they start with the same kinetic energy. At the top of the ramp, they must have the same gravitational potential energy, and therefore must be at the same height.

📄 Study AP Physics C: Mechanics, Unit 3.3: Conservation of Energy

15. The work done to stretch an ideal spring 20cm away from its equilibrium position is 8 Joules. How much work is required to stretch the spring 60cm?

A. 24 Joules

B. 72 Joules

C. 120 Joules

D. 400 Joules

Answer: Use the Work-Energy Theorem and the potential energy expression for springs to find the spring constant (k = 400 N/m). Then, plug that into the Work-Energy Theorem again with 0.6m to find work. Don't forget to convert to meters!

📄 Study AP Physics C: Mechanics, Unit 3.1: Work, Energy, and Power and Work-Energy Theorem

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🚗Unit 1 – Kinematics

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🎢Unit 3 – Work, Energy, & Power

3.1Work-Energy Theorem

3.2Forces and Potential Energy 🎢

3.3Conservation of Energy