Work, energy & power
The idea
When a force pushes an object through a distance, it transfers energy — that transfer is work: W = Fd cos θ, where θ is the angle between the force and the displacement. Work is measured in joules (1 J = 1 N·m). A force perpendicular to the motion does zero work, and a force opposing the motion does negative work, draining energy. You already know energy moves between forms; work is the mechanism by which forces move it.
The payoff is the work-energy theorem: the NET work done on an object equals its change in kinetic energy, where KE = ½mv². This often replaces a messy force-and-acceleration analysis with simple bookkeeping between two snapshots. Power then measures how fast the energy flows: P = W/t in watts (1 W = 1 J/s), or equivalently P = Fv for a force applied at speed v.
A common trap is thinking effort equals work. Holding a heavy barbell motionless feels exhausting, but physics says zero work is done on it because the displacement is zero. Likewise, carrying a bag horizontally at constant speed does no work against gravity, since the supporting force is perpendicular to the motion. Work demands a force component along the displacement.
Worked example
An electric motor lifts a 50 kg crate vertically through 12 m at constant speed, taking 15 s. How much work does the motor do on the crate, and what average power does it deliver?
- Constant speed means zero acceleration, so the lifting force exactly balances gravity: F = mg = 50 × 9.8 = 490 N upward.
- The force and the displacement point the same way (both upward), so θ = 0° and W = Fd = 490 × 12 = 5880 J.
- Interpret the number: the crate's kinetic energy never changed, so all 5880 J became gravitational potential energy — exactly mgh = 50 × 9.8 × 12.
- Divide by the time to get power: P = W/t = 5880/15 = 392 W.
- Sanity-check the scale: 392 W is about half a horsepower (746 W), a believable rating for a small hoist motor lifting 50 kg at a calm 0.8 m/s.
Answer. The motor does 5880 J of work on the crate and delivers an average power of about 392 W.
Check your understanding
- Why does a waiter carrying a tray across a level room do no work on the tray, even though his arm gets tired?
- How does the work-energy theorem let you skip finding acceleration in problems where the force varies in a complicated way?
- If the same crate were lifted in half the time, what would change about the work done and what would change about the power?
- When a force does negative work on an object, where does the object's energy go — and can you give a concrete example?
Build the foundations first
Work, energy & power builds on these concepts. If any feel shaky, start there.