AP Physics C: Mechanics, AP exams

Unit 3: Work, Energy, and Power

Unit 3 defines work as an integral of force over displacement, which lets the course handle position-dependent forces cleanly. Conservative forces, potential energy functions, and the relationship between force and the derivative of potential energy are central. Energy diagrams are a recurring representation.

Position: 3 of 7 units
Topics covered: 6 topics in this guide

What is covered

Topics inside this unit.

These topics describe the scope students most often review for this part of AP Physics C: Mechanics. Treat them as a study checklist rather than an exhaustive list of what a single exam form can sample.

Work as an integral: Computing work for variable forces, and reading work as area under a force-versus-position graph.
Kinetic energy and the work-energy relationship: Relating net work to the change in kinetic energy for both constant and variable forces.
Conservative forces and potential energy: Which forces have an associated potential energy function, and how that function is defined.
Force from potential energy: Recovering force as the negative derivative of the potential energy function.
Conservation of energy: Tracking mechanical energy through a system, including dissipation by nonconservative forces.
Power: Instantaneous and average power, and the relationship between power, force, and velocity.

Study tips

How to practice Work and Energy.

Section-specific guidance that follows from how this material is usually tested.

Practice both directions of the force and potential-energy relationship: differentiate a potential to get force, and integrate a force to get potential.
Use energy diagrams to identify equilibrium points and classify them as stable or unstable.
Choose energy over force methods when the force varies with position; it is usually far less work.

Where this fits

Unit 3: Work, Energy, and Power is 3 of 7 units in the AP Physics C: Mechanics guide. Use the full guide to balance it against everything else you have to review.

Back to the AP Physics C: Mechanics guide Official exam information

Sample Work and Energy questions

Practice questions, not yet expert-reviewed

Original practice questions written to the published framework for this section. No expert has reviewed them, and they are not taken from any official exam. Try each one before you open the answer.

Question 1Foundational
A variable force F(x) = 6x, with F in newtons and x in meters, acts on an object as it moves along the x-axis from x = 0 to x = 2.0 m. How much work does this force do on the object?
1. A3.0 J
2. B6.0 J
3. C12 J
4. D24 J
Show answer
Answer: C. 12 J
Work is the integral of force over displacement: the integral of 6x dx from 0 to 2.0 equals 3x^2 evaluated at 2.0, which is 12 J. The 24 J choice multiplies the force at the endpoint by the full displacement, which would only be valid for a constant force.
Key insight: For a variable force, work is the area under the force-versus-position graph.
Question 2Foundational
A tractor pushes a load with a constant 500 N force in the direction of motion while the load moves at a constant 4.0 m/s. What power does the tractor deliver to the load?
1. A125 W
2. B500 W
3. C1000 W
4. D2000 W
Show answer
Answer: D. 2000 W
Instantaneous power for a force along the velocity is P = Fv = (500 N)(4.0 m/s) = 2000 W. The 125 W choice divides force by speed instead of multiplying.
Key insight: At fixed power, force and speed trade off, which is why a vehicle must gear down to pull hard.
Question 3Intermediate
A particle moves along the x-axis in a region where its potential energy is U(x) = 3x^2 - 12x, with U in joules and x in meters. At what position is the particle in equilibrium?
1. A0 m
2. B2.0 m
3. C4.0 m
4. D6.0 m
Show answer
Answer: B. 2.0 m
The conservative force is F = -dU/dx = -(6x - 12), which vanishes at x = 2.0 m. Because the second derivative is positive there, U has a minimum and the equilibrium is stable, so a small displacement produces a restoring force.
Key insight: Force is the negative slope of the potential energy curve, so equilibrium sits where the curve is flat.
Question 4Intermediate
A 3.0 kg block sliding at 6.0 m/s along a level surface enters a rough patch and comes to rest after 4.0 m. Using g = 10 m/s^2, what is the coefficient of kinetic friction on the rough patch?
1. A0.23
2. B0.45
3. C0.90
4. D1.8
Show answer
Answer: B. 0.45
Setting the kinetic energy equal to the work done against friction gives (1/2)mv^2 = (mu)mgd, so mu = v^2/(2gd) = 36/(2 x 10 x 4.0) = 0.45 and the mass cancels. The 0.90 choice drops the factor of 2 that comes from the one half in the kinetic energy.
Key insight: Friction problems solved by energy avoid the intermediate acceleration entirely.
Question 5Advanced
A force directed along the x-axis has magnitude F(x) = 12/x^2, with F in newtons and x in meters. How much work does this force do on a particle that moves from x = 2.0 m to x = 6.0 m?
1. A2.0 J
2. B4.0 J
3. C6.0 J
4. D8.0 J
Show answer
Answer: B. 4.0 J
The integral of 12x^-2 dx is -12/x, so the work is (-12/6) - (-12/2) = -2 + 6 = 4.0 J. The 6.0 J choice extends the upper limit to infinity, and 8.0 J adds the two endpoint terms instead of subtracting them.
Key insight: Inverse-square forces do most of their work over the first part of the displacement, so the far limit contributes little.

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Unit 3: Work, Energy, and Power