Physics: Motion to AP Physics 1 · Module 4 of 8
Work, Energy & Power
Work, kinetic and potential energy, conservation of energy, springs, and power.
Work & Kinetic Energy
- Work W = Fd cos θ, where θ is the angle between the force and the displacement. A force perpendicular to the motion does no work.
- Kinetic energy KE = ½mv². The work–energy theorem: the net work done on an object equals its change in kinetic energy.
A 2.0 kg cart speeds up from 3.0 m/s to 5.0 m/s. How much net work was done on it?
Solution. W_net = ΔKE = ½(2.0)(5.0²) − ½(2.0)(3.0²) = 25 − 9 = 16 J.
Potential Energy & Conservation of Energy
- Gravitational potential energy U = mgh. Spring potential energy U = ½kx², where Hooke's law gives the spring force F = −kx.
- With no friction or other non-conservative forces, total mechanical energy (KE + U) is conserved. Friction converts mechanical energy into thermal energy.
A 2.0 kg ball is dropped from 5.0 m. How fast is it moving just before it hits the ground?
Solution. mgh = ½mv² → v = √(2gh) = √(2 × 9.8 × 5.0) ≈ 9.9 m/s. The mass cancels.
A spring with k = 200 N/m is compressed 0.10 m. How much energy does it store?
Solution. U = ½kx² = ½(200)(0.10)² = 1.0 J.
Power
- Power is the rate of doing work: P = W/t, measured in watts (1 W = 1 J/s). For a constant force along the motion, P = Fv.
A student lifts a 50 kg box 3.0 m in 5.0 s at constant speed. What average power does she supply?
Solution. W = mgh = 50 × 9.8 × 3.0 = 1,470 J. P = 1,470 / 5.0 = 294 W.
Check yourself
2 of this module's 5 quiz questions. Pick your answers, then check them in the app, with an explanation for every question.
1. You carry a box horizontally at constant velocity. How much work does your upward supporting force do on the box?
2. If an object's speed doubles, its kinetic energy: