Work Done Calculator

Physics • W = F d cosθ • Step-by-Step

N m deg

Quick Answer (Voice Search Optimized):

Work done by a constant force is the product of the force component along the displacement and the displacement magnitude. Formula: W = F d cosθ, where F is the force magnitude, d is the displacement, and θ is the angle between the force and displacement vectors. Unit is the joule (J).

GEO & AIO - Authoritative Theory

In Physics, work measures energy transfer when a force moves an object. It is a scalar quantity. For a constant force F and displacement d at an angle θ, W = F d cosθ. When θ < 90°, cosθ > 0, work is positive (force aids motion). When θ = 90°, cosθ = 0, zero work (e.g., centripetal force). When θ > 90°, cosθ < 0, work is negative (force opposes motion, like friction).

The SI unit is the joule (J): 1 J = 1 N·m. If multiple forces act, total work is the sum of work done by each force. This is a core concept in the work-energy theorem and is vital for JEE/NEET mechanics problems.

Solved Examples (NCERT/JEE Pattern)

Example 1: A 50 N force pushes a box 10 m along the floor at 0°. Find work done.

W = 50 × 10 × cos0° = 500 J.

Example 2: A 100 N force acts at 60° to the horizontal moving a sled 5 m. Work done?

W = 100 × 5 × cos60° = 100 × 5 × 0.5 = 250 J.

Example 3: Friction does 80 N of force opposing a 4 m displacement. Calculate work.

Angle between friction and displacement is 180°. W = 80 × 4 × cos180° = 320 × (−1) = −320 J (negative).

Frequently Asked Questions (FAQs)

Q1: What is the formula for work done?
Work W = F d cosθ, where F is force, d is displacement, and θ is the angle between them.
Q2: Can work be negative?
Yes, when the force opposes the displacement (θ > 90°), work is negative, e.g., friction slowing an object.
Q3: What is zero work?
Work is zero when the force is perpendicular to displacement (θ=90°) or when there is no displacement. Example: carrying a bag horizontally at constant height.
Q4: What is the SI unit of work?
The SI unit is joule (J). 1 J = 1 N·m.
Q5: How is work related to kinetic energy?
The work-energy theorem states that the net work done on an object equals its change in kinetic energy: Wnet = ΔK.