Work — Lifting a Box Against Gravity (Worked Example)

Given

• m = 25 kg

• h = 2.0 m

• lifted at constant speed

• g = 9.81 m/s²

Find

Work W done against gravity.

Principle

Work equals force times displacement in the direction of the force. Lifting at constant speed, the upward force equals the box's weight mg.

Formula

Solution

1. Weight: $F = mg = 25 \times 9.81 = 245.25\ \mathrm{N}$

2. Work: $W = F \times d = 245.25 \times 2.0$

3. Calculate: $W = 490.5\ \mathrm{J} \approx 491\ \mathrm{J}$

Unit check

N × m = J. Force times distance gives energy — consistent.

What this means physically

491 J goes into the box as gravitational potential energy. Set it down and that same energy must be absorbed — which is why dropping it from 2 m would hurt.