Work Formula
The work formula W = Fd·cos(θ) calculates the work done by a force over a distance.
Includes angle consideration and step-by-step examples.
The Formula
Work is the energy transferred when a force moves an object over a distance. When the force is in the same direction as the motion, cos(θ) = 1, simplifying to W = Fd.
Variables
| Symbol | Meaning |
|---|---|
| W | Work done (measured in joules, J) |
| F | Applied force (measured in newtons, N) |
| d | Distance moved (measured in meters, m) |
| θ | Angle between the force and the direction of motion (degrees) |
Example 1
A person pushes a box with 50 N of force across 8 m of floor. The force is in the direction of motion. How much work is done?
θ = 0° so cos(0°) = 1
W = Fd·cos(θ) = 50 × 8 × 1
W = 400 J
Example 2
A worker pulls a sled with a rope at 30° above the horizontal. The force in the rope is 200 N and the sled moves 15 m. How much work is done?
θ = 30° so cos(30°) = 0.866
W = Fd·cos(θ) = 200 × 15 × 0.866
W = 2,598 J (approximately 2,600 J)
When to Use It
Use the work formula to calculate energy transferred by a force.
- Pushing, pulling, or lifting objects over a distance
- Calculating energy input or output in mechanical systems
- When force is applied at an angle to the direction of motion
- Determining whether a force does positive, negative, or zero work