Practice
Work and energy
Kinetic and potential energy, work by a force at an angle, the work-energy theorem, and conservation of energy for falls and springs.
The skill
Work is energy transferred by a force over a distance, and only the component of the force parallel to the displacement counts: . To find a speed, add the work done by every force, positive or negative, and set the sum equal to . When only conservative forces act inside the system, you can track energy stores instead, and , with total mechanical energy constant. The common slips are forgetting that friction does negative work and counting gravity twice, once as work and again as potential energy.
A worked example
A 5.5 kg box starts from rest. A horizontal 22 N push moves it 6.3 m across a level floor, while kinetic friction exerts a constant 11 N on it.
What is the box's speed at the end of the 6.3 m, in m/s? Give your answer to three significant figures.
Solution
- Net work is the sum of the work done by each force: the push does +138.6 J and friction does −69.3 J, for 69.3 J.
- : 1/2 (5.5) v² − 0 = 69.3, so v = √(2 × 69.3 ÷ 5.5) = 5.02 m/s.
Answer: 5.02