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3.2 Work

Part of Work, Energy, and Power in AP® Physics 1: Algebra-Based. Read the opening section, then create a free account for the full interactive lesson, practice, and progress tracking.

Work

Work is defined as the process of transferring energy to or from an object by applying a force over a distance. When a force moves an object in the direction of that force, work is done on the object, and energy is transferred to it. Only the component of force exerted parallel to the direction of displacement will do work. Work can be positive, negative, or 0 depending on the angle of the force. Work is a scalar, measured in Joules (J), and represented with the variable W.

W=FdcosθW = Fd cos\theta
  • W{W} represents the work done by the force
  • F{F} is the force
  • d{d} is the displacement of an object when the force was exerted
  • θ{\theta} is the angle between the direction of displacement and the direction of force

The cosine part of the equation is important, as it tells us that if the force acts in the opposite direction of the displacement, the work done will be negative as cos(180°)=-1; however, if the force and displacement are in the same direction, the work done will be positive as cos(0°)=1. Also, if the force and displacement are perpendicular, no work will be done as cos(90°)=0. This has an important implication that gravity does no work if an object slides horizontally.

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