Work, Energy and Power

The work done by a constant force $F$ acting on a body is defined as the scalar (dot) product of the force and the resulting displacement: $W=\vec{F}\cdot \vec{d}=Fd\cos \theta$, where $\theta$ is the angle between the two vectors. Work is a scalar quantity with SI unit the joule (J), equal to $1\mathrm{N}\mathrm{m}=1\mathrm{kg}{\mathrm{m}}^2{\mathrm{s}}^{-2}$.

The sign of $W$ follows directly from $\co

An object's kinetic energy is the energy it possesses by virtue of its motion, $KE=\frac{1}{2}m{v}^2$, a scalar quantity that — unlike work — can never be negative. The work-energy theorem links the two directly: the work done by the net force on a body equals its change in kinetic energy, $W_{net}=K{E}_f-K{E}_i$. This holds for a variable force just as for a constant one — writing $F = m,d

A collision is an event in which two bodies exert large, mutually interactive forces on each other for a relatively short time, redistributing momentum and energy between them. Linear momentum is conserved in every collision, elastic or not, provided no external force acts on the colliding pair — this follows from Newton's third law, since the forces the two bodies exert on each other are

Power measures the rate at which work is done or energy is transferred. Average power over a time interval is $P_{avg}=W/t$; the more general instantaneous power is $P=\frac{dW}{dt}=\vec{F}\cdot \vec{v}=Fv\cos \theta$, the dot product of the applied force and the instantaneous velocity. Power is a scalar, with SI unit the watt (W), equal to $1\mathrm{J}{\mathrm{s}}^{-1}$; the commercia