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).