Energy

Work

transferring energy with a force

Pushing an object through a distance does work on it, and that work is the energy it gains.

mechanics A 4 N push over 3 m does a clean 12 J of work.

Example

Pushing an object through a distance does work on it, and that work is the energy it gains. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Work is force times distance

Pushing something along transfers energy to it. When the push is along the motion, the work done is the force times the distance it moves through, and that work shows up as energy gained.

W=F dW = F\,d
Pushing a cart does workA cart on flat ground with a force arrow pushing it forward.mF

A worked value

Pushing with 4 newtons over 3 metres does 4 times 3, or 12 joules of work — that much energy is added to the cart.

W=F d=4 N ⋅ 3 m=12 JW = F\,d = 4\ \text{N} \,\cdot\, 3\ \text{m} = \hl{12}\ \text{J}

Same distance, more force, more work

Hold distance fixed. A larger push transfers more energy over the same path.

FdW2 N3 m6 J4 N3 m12 J6 N3 m18 J\begin{array}{c|c|c}F & d & W \\ \hline 2\ \text{N} & 3\ \text{m} & 6\ \text{J} \\ 4\ \text{N} & 3\ \text{m} & 12\ \text{J} \\ 6\ \text{N} & 3\ \text{m} & 18\ \text{J}\end{array}

Same force, more distance, more work

Hold force fixed. Let the push act over more distance and it transfers more energy.

FdW4 N1 m4 J4 N2 m8 J4 N3 m12 J\begin{array}{c|c|c}F & d & W \\ \hline 4\ \text{N} & 1\ \text{m} & 4\ \text{J} \\ 4\ \text{N} & 2\ \text{m} & 8\ \text{J} \\ 4\ \text{N} & 3\ \text{m} & 12\ \text{J}\end{array}