Work Done (Force at an Angle) Calculator

Formula first

Overview

Work done is defined as the product of the component of force acting in the direction of displacement and the displacement itself. The cosine component effectively isolates the magnitude of the force that contributes to energy transfer, while the component perpendicular to the motion does no work. This is a fundamental concept in energy conservation and mechanical analysis.

Symbols

Variables

W = Work Done, F = Force, d = Displacement, $\theta$ = Angle (degrees)

Apply it well

When To Use

When to use: Use this when a force is pulling or pushing an object at an incline relative to the path of travel.

Why it matters: It explains why pulling a suitcase at an angle requires less effective effort than dragging it straight, and how energy is conserved in mechanical systems.

Avoid these traps

Common Mistakes

• Using the sine component instead of cosine.
• Confusing the angle with the one provided relative to the vertical axis instead of the displacement vector.

One free problem

Practice Problem

A box is pulled 5 meters along a horizontal floor by a force of 20 N applied at an angle of 30 degrees to the horizontal. Calculate the work done.

Solve for: $W$

Hint: Use the formula W = Fd cos(theta) and ensure your calculator is in degree mode.

The full worked solution stays in the interactive walkthrough.

References

Sources

1. A-Level Physics: Fundamentals of Energy and Work (OCR/AQA/Edexcel Curricula)
2. AQA/OCR/Edexcel Physics A-Level Specification (Mechanics)