Physics Energy

Work & the Work-Energy Theorem

Compute work done by a constant force (W = F·d·cosθ) or apply the work-energy theorem to find work from change in kinetic energy. Step-by-step solutions with diagrams.

W = F·d·cosθ

W_net = ΔKE

KE bar chart

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Inputs

Mode

Force F (N)

Displacement d (m)

Angle θ between F and d (degrees)

Mass m (kg)

Initial speed v₀ (m/s)

Final speed v (m/s)

Net work W_net (J)

Initial KE (J)

Final KE (J)

Results

Select a mode and enter values above.

Diagram

Step-by-Step Solution

Work & the Work-Energy Theorem

Work is done when a force causes displacement in the direction of the force. Only the component of force parallel to the displacement does work — hence the cosθ factor.

The work-energy theorem states that the net work done on an object equals its change in kinetic energy: W_net = ΔKE = ½mv² − ½mv₀².

W = F·d·cosθ W_net = ½mv² − ½mv₀²

If θ = 90°, the force is perpendicular to motion and does zero work (e.g., normal force on horizontal surface).

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