Work and kinetic energy
Calculate energy transferred by a force and compare moving objects.
Before you begin
- Force and distance
- Squaring and unit conversions
Calculate work for a force along the displacement
For a constant force acting along an object's displacement, work done is force multiplied by displacement. The unit newton-metre is a joule. A force perpendicular to displacement does no work on the object in this model. If several forces act, their individual energy transfers and signs matter; the work of the resultant equals the change in kinetic energy.
Use the squared-speed relationship
Kinetic energy depends on both mass and speed: Eₖ = ½mv². Use kilograms and metres per second to obtain joules. Doubling mass doubles the kinetic energy at fixed speed, but doubling speed multiplies it by four. This nonlinearity explains why comparing speeds alone can underestimate differences in energy.
Worked example
Find the kinetic energy of a 2 kg trolley moving at 3 m/s.
Show the worked solution
- Substitute the mass and speed into ½mv².
- Square the speed first: 3² = 9.
- Calculate 0.5 × 2 × 9.
9 J.
Try it yourself
If an object's speed triples and mass stays constant, what happens to kinetic energy?
Common mistakes
- Square the numerical speed before multiplying by mass.
What can you explain now?
A constant 12 N force acts along a 5 m displacement. Calculate its work.
Compare with the explanation
60 J.
The force and displacement have the same direction, so W = 12 × 5. A different angle would require accounting for the force component along the displacement.
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