Energy

Kinetic Energy

the energy of motion

A moving object carries energy equal to one half its mass times its speed squared; squaring the speed means fast objects carry a lot.

Example

A moving object carries energy equal to one half its mass times its speed squared — and squaring the speed means fast objects carry a lot. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Kinetic energy is the energy of motion

A moving object carries energy. It is one half the mass times the speed squared. The speed is squared, so going twice as fast carries four times the energy.

KE=12 m v2KE = \tfrac{1}{2}\,m\,v^{2}
A moving cart carries kinetic energyA cart on flat ground with a velocity arrow.mv

A worked value

A 2 kilogram cart at 4 metres per second has speed squared 16, so the kinetic energy is one half times 2 times 16, or 16 joules.

KE=12 m v2=12 ⋅ 2 kg ⋅ 16=16 JKE = \tfrac{1}{2}\,m\,v^{2} = \tfrac{1}{2} \,\cdot\, 2\ \text{kg} \,\cdot\, 16 = \hl{16}\ \text{J}

Same speed, more mass, more kinetic energy

Hold speed fixed. A heavier cart carries more kinetic energy in direct proportion to mass.

mvKE1 kg4 m/s8 J2 kg4 m/s16 J3 kg4 m/s24 J\begin{array}{c|c|c}m & v & KE \\ \hline 1\ \text{kg} & 4\ \text{m}/\text{s} & 8\ \text{J} \\ 2\ \text{kg} & 4\ \text{m}/\text{s} & 16\ \text{J} \\ 3\ \text{kg} & 4\ \text{m}/\text{s} & 24\ \text{J}\end{array}

Same mass, speed changes energy by a square

Hold mass fixed. Doubling speed makes four times the kinetic energy, because the speed is squared.

mvKE2 kg2 m/s4 J2 kg4 m/s16 J2 kg6 m/s36 J\begin{array}{c|c|c}m & v & KE \\ \hline 2\ \text{kg} & 2\ \text{m}/\text{s} & 4\ \text{J} \\ 2\ \text{kg} & 4\ \text{m}/\text{s} & 16\ \text{J} \\ 2\ \text{kg} & 6\ \text{m}/\text{s} & 36\ \text{J}\end{array}
mechanics A 2 kg cart at 4 m/s gives a clean 16 J of kinetic energy.