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Work in Physics

Sep 11, 2025

Overview

The lecture covers the concept of work done in physics, the calculation of work for different forces (applied, friction, gravity, normal, net), and applications on horizontal and inclined planes, emphasizing the correct use of angles in work calculations.

Definition of Work Done

  • Work done is the product of a force and the displacement parallel to the force.
  • The general formula: Work = Force × Displacement × cos(θ), where θ is the angle between the force and displacement.

Work Done on a Horizontal Surface Example

  • A 10 kg block is pulled with a 40 N force over 5 m; friction force is 20 N.
  • Applied force: Work = 40 × 5 × cos(0°) = 200 J (cos(0°)=1; force and displacement in same direction).
  • Frictional force: Work = 20 × 5 × cos(180°) = -100 J (cos(180°)=-1; friction opposes motion).
  • Gravity: Work = 98 × 5 × cos(90° or 270°) = 0 J (gravity acts perpendicular to horizontal displacement).
  • Normal force: Work = 98 × 5 × cos(90°) = 0 J (normal force is also perpendicular).
  • Net work: Net force = 40 - 20 = 20 N; Net work = 20 × 5 × cos(0°) = 100 J; or sum of individual works.

Work Done on an Inclined Plane Example

  • Block on a 30° incline, pulled with 80 N up the incline, friction is 12 N, displacement is 5 m.
  • Draw a free body diagram showing applied force, friction, normal force (perpendicular to incline), and gravity (vertical).
  • Gravity splits into two components: parallel (mg sinθ), perpendicular (mg cosθ).

Calculations:

  • Applied force: Work = 80 × 5 × cos(0°) = 400 J.
  • Friction: Work = 12 × 5 × cos(180°) = -60 J.
  • Gravity (parallel component):
    • FG_parallel = 10 × 9.8 × sin(30°) = 49 N.
    • Work = 49 × 5 × cos(180°) = -245 J.
  • Normal force: Work = 84.87 × 5 × cos(90°) = 0 J (normal force does no work).
  • Net work: Net force = 80 - 49 - 12 = 19 N; Net work = 19 × 5 × cos(0°) = 95 J; or sum component works.

Key Terms & Definitions

  • Work — Energy transferred when a force moves an object over a displacement, W = F × d × cos(θ).
  • θ (theta) — Angle between the direction of force and direction of displacement.
  • Frictional Force — Force opposing motion between surfaces in contact.
  • Normal Force — Force perpendicular to the surface, supporting the weight of an object.
  • Force of Gravity (FG) — The weight of an object, FG = m × g.
  • Inclined Plane — A flat surface tilted at an angle to the horizontal.
  • FG_parallel — Component of gravity along an incline, FG × sin(θ).
  • FG_perpendicular — Component of gravity perpendicular to an incline, FG × cos(θ).

Action Items / Next Steps

  • Review your notes on free body diagrams and vector components.
  • Prepare for the next lecture on conservation of mechanical energy.
  • Practice calculating work done for multiple forces on different planes.

Full transcript