Forces and force diagrams

By the end of this lesson

By the end you can list every force acting on an object and draw a clear, labelled force diagram, the first step in almost every mechanics question.

Forces and particles

A force is a push or a pull. It's measured in newtons, written N. (Roughly, 1 N is the weight of a small apple.)

In mechanics we often model an object as a particle: we pretend all its mass sits at a single point and ignore its size and shape. On a diagram, a particle is just a dot.

Every force is drawn as an arrow starting at the dot:

the arrow's direction shows which way the force acts;
the label says which force it is, or how big.

Definition

Force diagram

A force diagram shows the object and every force acting on it, each as a labelled arrow.

Only forces acting on the object go in. Forces the object exerts on other things don't.

The forces you'll meet

Force	Symbol	Where it comes from	Direction
Weight	$mg$ or $W$	the Earth's gravity	vertically down
Normal reaction	$R$	a surface the object touches	perpendicular (at $90°$ ) to the surface, pushing away from it
Tension	$T$	a taut string or rope	along the string: it pulls the object towards the string, so draw the arrow from the object along the string
Friction	$F$	a rough surface	along the surface, against sliding
Applied force	$P$	a push or pull from outside	whatever the question says

Weight is $mg$ : the mass $m$ in kilograms times $g$ , the acceleration due to gravity. In 9709 take $g = 10\ \text{m s}^{-2}$ , so a 3 kg mass has weight $30$ N.

Smooth means no friction. Rough means there may be friction.

How to draw one

Draw a dot for the object.
Weight first: an arrow straight down, labelled $mg$ .
Touching anything? For each surface it touches, add a normal reaction at $90°$ to that surface. If the surface is rough, add friction along it too.
Strings? For each taut string attached, add a tension arrow along the string.
Anything else the question mentions, like a push $P$ .

Don't draw an arrow for "motion" or "speed". Moving isn't a force.

Worked example: Example: a parcel on a rough table

A parcel rests on a rough horizontal table. A string pulls it horizontally to the right. List the forces on the parcel and their directions.

Have a go first?

Name the forces

Multiple choiceQuestion 1 · Recall

Short answerQuestion 2 · Recall

Short answerQuestion 3 · Recall

Multiple choiceQuestion 4 · Apply

Answer the 4 questions above to continue.