Physics Formula
Mechanical Work Formula
Calculates work when force acts through a displacement.
Formula Summary
Mechanical Work
Calculates work when force acts through a displacement.
- Category
- Physics
- Equation
- W = Fd cos θ
- Calculator
- Use Mechanical Work Calculator →
Equation
W = Fd cos θ
Variables
- W = work
- F = force
- d = displacement
- θ = angle
Units
- Work: Joules (J)
- Force: Newton (N)
- Displacement: meters (m)
- Angle: degrees or radians
When To Use This Formula
Use this formula when calculating energy transferred by a force that causes an object to move through a displacement.
Rearranged Equations
- F = W / (d cos θ)
- d = W / (F cos θ)
How to Use This Formula
- Identify the known values from the problem statement.
- Convert all values into compatible units.
- Substitute the values into the equation and calculate the result.
- Check that the final answer has the correct unit and meaning.
Explanation
Mechanical work measures energy transferred when a force causes an object to move through a displacement. The amount of work depends on force, distance, and the angle between them.
Worked Example
A 10 N force moves an object 5 m in the same direction. Work done is 10 × 5 × cos(0°) = 50 J.
Common Mistakes
- Ignoring the angle between force and displacement.
- Confusing work with force alone.
- Using incorrect units instead of joules.
Applications
- Machine and mechanical system analysis.
- Energy transfer calculations.
- Physics experiments involving forces and motion.