Work, Energy, and Power practice quiz

Key ideaW = ∫F · dr (in one dimension, ∫F_x dx): integrate the force component along the path, or find the area under F(x).

Common mistakeUsing Fd when the force varies, or ignoring the angle between force and displacement.

Key ideaThe net work done on an object equals its change in kinetic energy, ΔK, whatever forces are involved.

Common mistakeCounting a force twice: once as work and again as a change in potential energy.

Key ideaFor a conservative force, F = −dU/dx. Equilibrium is where the slope of U is zero; a minimum is stable and a maximum is unstable.

Common mistakeDropping the minus sign, which points the force uphill on the U(x) graph instead of downhill.

Key ideaK + U stays constant when only conservative forces do work. Otherwise, the work done by friction or other forces accounts for the change.

Common mistakeUsing energy conservation across an inelastic collision, where kinetic energy is lost.

Key ideaP = dW/dt = F·v. The average power is the total work divided by the time.

Common mistakeUsing the average force or speed to find an instantaneous power.