Work Done
Work done by a force over a distance.
Formula
Variables
Example
Pushing 50 N over 4 m in the direction of motion: W = 50·4 = 200 J.
How it works
This formula calculates how much energy a force transfers to an object as it moves. Only the part of the force acting along the direction of motion contributes to work, which is why the force is multiplied by cosθ: if the force is not perfectly aligned, only its forward component does useful work. When the force is perpendicular to the motion, cosθ = 0, so no work is done.
When to use it
Use this when a force causes an object to move and you need the energy transferred by that force, such as pushing, pulling, lifting, or dragging. It is especially useful when the force is applied at an angle, because you must account for only the component in the direction of motion.
Worked example, step by step
A student pulls a sled with a force of 80 N at an angle of 30° to the horizontal. The sled moves 6 m. Use W = Fd cosθ. W = 80 × 6 × cos30° W = 480 × 0.866 W ≈ 415.7 J Final answer: W ≈ 416 J
Common mistakes to avoid
- Using the full force even when it acts at an angle instead of multiplying by cosθ
- Forgetting that distance must be in metres to get work in joules
- Using the angle between the force and the floor when the problem gives a different angle between force and motion
Did You Know?
In physics, carrying a heavy box across a level floor does zero work — no motion in the direction of the force.
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