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How It Works
Work measures energy transferred by a force. The work-energy theorem (W = ½m(v₂² − v₁²)) links work to changes in kinetic energy. The force-distance formula (W = F·d·cosθ) calculates work when a constant force acts through a displacement. The SI unit is the joule (J).
Example Problem
A 100 N force pushes a crate 5 m along a floor at a 30° angle to the horizontal. How much work is done?
- W = 100 × 5 × cos(30°) = 500 × 0.866
- W = 433 J
Frequently Asked Questions
When is work zero even though a force is applied?
When the force is perpendicular to the displacement (θ = 90°), cos(90°) = 0 and no work is done. A person carrying a box horizontally does no work on the box (the lifting force is vertical).
Can work be negative?
Yes. Negative work means energy is removed from the object. Friction does negative work by slowing objects down. This corresponds to θ > 90° between force and displacement.
What is the difference between work and power?
Work is the total energy transferred (in joules). Power is the rate at which work is done (joules per second, or watts). Doing 1,000 J of work in 10 s requires 100 W of power.
Related Calculators
- Power Calculator — find the rate of doing work.
- Kinetic Energy Calculator — calculate the energy of motion.
- Potential Energy Calculator — find energy stored by position.
- Force Equation Calculator — calculate the force component of a work equation.
- Energy Unit Converter — convert work and energy between joules, calories, and BTU.
Reference: Lindeburg, Michael R. 1992. Engineer In Training Reference Manual. Professional Publication, Inc. 8th Edition.