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Mechanics · Work, energy & power

Chapter 1 · 4

The idea

Kinetic and potential energy

Kinetic energy ½mv² and gravitational potential energy mgh, the work–energy principle (the work done by the resultant force equals the change in kinetic energy), and conservation of mechanical energy — including motion along a smooth curved path, where only the overall energy change matters.

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Mechanics · Work, energy & power

Kinetic and potential energy

Kinetic energy ½mv² and gravitational potential energy mgh, the work–energy principle (the work done by the resultant force equals the change in kinetic energy), and conservation of mechanical energy — including motion along a smooth curved path, where only the overall energy change matters.

Why it works

The two energies

A moving object has kinetic energy KE=12mv2,\text{KE} = \tfrac12 mv^2, and an object at height hh above some reference level has gravitational potential energy PE=mgh,\text{PE} = mgh, both measured in joules. Throughout Paper 4 take g=10 m s−2g = 10\text{ m s}^{-2}.

The work–energy principle

The work done by the resultant force on an object equals the change in its kinetic energy: Wnet=12mv2−12mu2.W_{\text{net}} = \tfrac12 mv^2 - \tfrac12 mu^2. This is often the quickest route to a final speed, because it links force and distance directly to speed without needing the time or the acceleration.

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