Work, Energy, and Power

What this unit covers

The topics below follow the published Physics 1 course framework for Unit 3. This unit is worth 18–23% of the exam, so budget your time against that rather than against how long the unit takes to teach.

Lessons in this unit

• Work & the Work–Energy Theorem13 min · 3 objectivesCompute work as W = Fd cosθ and identify its sign · Recognize when a force does zero work · Apply the work–energy theorem, W_net = ΔKE
• Kinetic & Potential Energy13 min · 3 objectivesCompute kinetic energy with KE = ½mv² · Compute gravitational potential energy with PE = mgh · Compute elastic potential energy stored in a spring, ½kx²
• Conservation of Energy14 min · 3 objectivesState the conservation of mechanical energy for frictionless systems · Convert between potential and kinetic energy in falls, ramps, and swings · Account for energy lost to friction as thermal energy
• Power12 min · 3 objectivesDefine power as the rate of doing work, P = W/t · Relate power to force and velocity, P = Fv · Compare machines by how quickly they deliver energy

Formulas in Unit 3

Every term in Unit 3

All 21 terms we publish for Work, Energy, and Power, with definitions. Reading them through is the fastest way to find the ones you cannot define — then drill those in cram mode until you can produce them without the prompt.

Power

Rate of energy transfer, P = W/t = Fv. Same work done faster means more power, not more energy.

Work

W = Fd cos θ, where θ is the angle between force and displacement. A force perpendicular to motion does no work.

Work from a graph

The area under a force-position graph. This is how work is found when the force is not constant, where W = Fd fails.

Kinetic energy

KE = ½mv². Doubling speed quadruples kinetic energy, which is why stopping distance grows so fast with speed.

Work-energy theorem

Net work equals change in kinetic energy. Valid whether or not forces are conservative.

Gravitational potential energy

PE = mgh near Earth's surface, measured from a chosen reference height. Only changes in PE are physically meaningful.

Elastic potential energy

PE = ½kx², where x is displacement from the natural length. Compression and extension store the same energy.

Hooke's law

F = −kx. The negative sign shows the restoring force opposes the displacement.

Conservative vs non-conservative forces

Conservative forces (gravity, spring) store energy recoverably and do path-independent work; friction and drag dissipate it.

Conservation of mechanical energy condition

KE + PE is constant ONLY when non-conservative forces do no work. With friction present, use energy accounting including thermal energy instead.

Energy bar charts

Track energy between states, including thermal energy generated by friction, so that total energy is conserved even when mechanical energy is not.

Choosing energy or kinematics

Energy methods are best when force varies or the path is complex; kinematics needs constant acceleration and gives timing information energy cannot.

Sign of work

Positive when force has a component along the displacement, negative when opposed. Friction on a sliding block does negative work.

Work done by a spring

The area under the F vs x line, which is ½kx² since the force grows linearly. Using F = kx times x would double-count.

Energy accounting with friction

Initial energy = final energy + friction force × path length. Note it is path LENGTH, not displacement — friction is not conservative.

Choosing the reference height

Any height may be defined as zero potential energy; only differences matter. Pick the lowest point of the motion to keep terms positive.

Energy in a pendulum

All potential at the extremes, all kinetic at the bottom. Maximum speed occurs where potential energy is minimum.

Power in terms of velocity

P = Fv, so a car at constant speed against constant drag has power proportional to speed and does no net work.

Efficiency

Useful energy output divided by total energy input. Always below 1 because some energy becomes thermal.

Why energy methods ignore the path

Conservative forces do path-independent work, so only endpoints matter — which is what makes a curved frictionless track solvable without calculus.

Escape and binding energy qualitatively

An object bound in a gravitational well has negative total energy; supplying enough energy to reach zero lets it escape.

What examiners penalize here

• Before computing work, check the angle between the force and the displacement. Perpendicular forces (normal force on a flat surface, gravity in horizontal motion, tension in circular motion) do exactly zero work — a favorite AP trap.
• You may place the h = 0 reference wherever it is most convenient — the floor, the tabletop, the ground below a cliff. Only the *change* in height between start and finish affects the physics, so choose the level that makes the arithmetic simplest.
• If a problem mentions friction or air resistance, mechanical energy is *not* conserved — the "missing" energy became heat. Write KE_i + PE_i = KE_f + PE_f + E_thermal and treat the thermal term as the energy removed.
• Remember that power and energy are different quantities: energy (joules) is the total transferred, power (watts) is the rate. A question asking "how quickly" or "per second" is about power; "how much total" is about energy or work.

Practice Physics 1

Our practice bank is drawn from across the whole course rather than filtered to one unit, which is closer to how the exam asks anyway — it will not tell you which unit a question is testing.

Questions about this unit

All 8 units of AP Physics 1: Algebra-Based

1. Unit 1 · Kinematics
2. Unit 2 · Force and Translational Dynamics
3. Unit 3 · Work, Energy, and Power
4. Unit 4 · Linear Momentum
5. Unit 5 · Torque and Rotational Dynamics
6. Unit 6 · Energy and Momentum of Rotating Systems
7. Unit 7 · Oscillations
8. Unit 8 · Fluids