Vectors and Forces

Free-Body Diagram

name every force on one object

A free-body diagram draws every force on one object as an arrow from its centre, so the net force is just the arrows added up.

Example

A free-body diagram draws every force on a single object as an arrow from its centre, so the net force is just the arrows added up. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

First force: weight

A block of mass 2 kilograms sits on the floor. Gravity pulls it down with a weight of mass times gravity: 2 times 10 is 20 newtons, downward.

W=m g=2 kg ⋅ 10 m/s2=20 NW = m\,g = 2\ \text{kg} \,\cdot\, 10\ \text{m}/\text{s}^{2} = \hl{20}\ \text{N}
The weight pulling downAn isolated block with a single arrow pointing straight down.mW

Second force: the floor pushes back

The floor pushes up with a normal force. The block does not sink or rise, so the up and down forces balance: the normal force is 20 newtons, upward.

N=W=20 NN = W = \hl{20}\ \text{N}
Weight balanced by the normal forceA block with a downward weight arrow and an equal upward normal arrow.mWN

More mass means more weight

Keep gravity at 10 metres per second squared. More mass makes a larger downward weight.

mgW1 kg10 m/s210 N2 kg10 m/s220 N3 kg10 m/s230 N\begin{array}{c|c|c}m & g & W \\ \hline 1\ \text{kg} & 10\ \text{m}/\text{s}^{2} & 10\ \text{N} \\ 2\ \text{kg} & 10\ \text{m}/\text{s}^{2} & 20\ \text{N} \\ 3\ \text{kg} & 10\ \text{m}/\text{s}^{2} & 30\ \text{N}\end{array}

Third force: the push

Someone pushes the block sideways with 6 newtons to the right. Nothing balances it horizontally.

P=6 N (right)P = \hl{6}\ \text{N (right)}
All three forces on the blockA block with balanced up and down arrows and a rightward push arrow.mWNP

Add them up: the net force

Up and down cancel, so the net force is just the push: 6 newtons to the right. That is what will accelerate the block.

Fnet=6 N (right)F_{\text{net}} = \hl{6}\ \text{N (right)}
The net forceA block with the up and down arrows cancelling and one rightward net-force arrow.mWNnet
mechanics With a 2 kg block and g = 10, the weight and normal force are clean 20 N arrows and the net force is the leftover push.