Work Formula
What is the Work Formula?
In physics, work is done when a force causes an object to move — but only the component of the force in the direction of motion counts. If force and displacement are perfectly aligned (θ = 0°), cos(0°) = 1, and the formula simplifies to the familiar W = Fd.
If a force acts but causes no displacement at all — like pushing against an immovable wall — the work done is exactly zero, no matter how hard you push, because d = 0.
What Each Variable Means
When to Use It
- Calculating the energy transferred by a force over a distance
- Analyzing situations where force and motion aren't perfectly aligned
- As part of the work-energy theorem relating work to change in kinetic energy
Step-by-Step Example
Problem: A force of 50 N pushes a box horizontally over 10 m. What is the work done?
θ = 0°, so cos(0°) = 1.
cos(0°) = 1Multiply force, distance, and cos(θ).
W = 50 × 10 × 1Interactive Calculator
Common Mistakes
Mistake: Forgetting the cos(θ) term when force and motion aren't parallel.
Fix: If the force acts at an angle to the direction of motion, only the cos(θ) component contributes — leaving it out overestimates the work done.
Mistake: Assuming pushing hard always means doing work.
Fix: If there's no displacement (d = 0), the work done is zero regardless of how much force is applied — work requires actual motion in the force's direction.
Practice Questions
A force of 20 N moves an object 5 m in the same direction as the force. Find the work done.
A 30 N force acts at 60° to a 4 m displacement. Find the work done.
Hint: cos(60°) = 0.5.
Frequently Asked Questions
Why is work zero when pushing against a wall?
Because the wall doesn't move — d = 0, and multiplying anything by zero gives zero, regardless of how much force is applied.
Can work be negative?
Yes — if the force has a component opposite to the direction of motion (θ between 90° and 180°), cos(θ) is negative, meaning the force removes energy rather than adding it (like friction slowing something down).