BitWithBite
Mechanics · Quick Reference
Work Cheat Sheet
In one line: in physics, 'work' has a precise meaning: force applied over a distance — simply pushing hard without moving anything technically accomplishes no work at all.
Key Ideas
1Work Definition. Work is done when a force causes displacement in the direction of that force: W = F*d*cos(theta), where theta is the angle between the force and displacement.
2Positive, Negative, and Zero Work. Work is positive when force and motion align, negative when they oppose (like friction), and zero when force is perpendicular to motion or there's no displacement.
3Units of Work. Measured in joules (J), where 1 joule = 1 newton x 1 meter.
4Work Done Against Gravity. Lifting an object at constant speed requires work equal to W = m*g*h, where h is the height raised.
5Work-Energy Theorem. The net work done on an object equals its change in kinetic energy: W_net = (change in KE).
Worked Examples
A 10 N force pushes a box 5m in the same direction as the force. Find the work done.
50 J
A 20 N force is applied at 60° to the direction of motion, moving an object 4m. Find the work done. (cos(60°)=0.5)
40 J
Find the work done lifting a 5 kg object 2m straight up (g=10 m/s^2).
100 J
Formulas
W = F*d*cos(theta)
W (against gravity) = m*g*h
Practice Yourself
A 15 N force pushes an object 3m in the same direction. Find work done.
45 J
Find the work to lift a 2 kg object 5m (g=10).
100 J
A force is applied perpendicular to an object's motion. Find the work done.
0 J (cos(90°)=0)