Force diagrams

In a nutshell

Newton's first law states that an object will remain stationary or in motion unless acted on by an external resultant force. Forces act on objects, which results in a change in their velocity. Forces can be shown using a force diagram, where it is possible to add up all the forces acting on an object and calculate a resultant force.

Variable definitions

QUANTITY NAME	SYMBOL	UNIT NAME	UNIT
$Force$	$F$	$Newton$	$N$
$Weight$	$W$	$Newton$	$N$
$Friction$	$F$	$Newton$	$N$
$Normal \ contact \ force$	$N$	$Newton$	$N$
$Tension$	$T$	$Newton$	$N$

Newton's first law

Newton's first law of motion states the following:

"A object remains stationary, or in motion at a constant speed in the same direction, unless acted upon by an external resultant force."

This means that a stationary object will remain stationary unless a force acts on it. Similarly, an object moving at constant velocity will continue to move at that velocity unless a force acts on it.

Force diagrams

A force diagram displays all the forces acting on an object. Forces are represented as arrows pointing in the direction they act on the object.

Maths; Forces and motion; KS5 Year 12; Force diagrams

Forces acting upon a box, for example: $a =$ normal reaction, $b=$ tension, $c=$ weight, $d=$ friction.

You can use force diagrams to find the resultant force. Force arrows pointing in the same direction add together. Force arrow pointing in opposite directions subtract from one another. The sum of all forces is the resultant force.

procedure

1.	Label all the forces acting upon an object.
2.	Find the sum of the forces.
3.	Determine the magnitude and direction of the resultant force. Give your answer in Newtons ( $N$ ).

Resultant force

The resultant force ( $R\uparrow$ ) is the sum of all forces acting on an object. An object will accelerate according to the magnitude and direction of the resultant force.

Example 1

Below is the force diagram of an object. Calculate the resultant force ( $R \uparrow$ ) acting on the object.

Maths; Forces and motion; KS5 Year 12; Force diagrams

Find the value of the vertical force by adding forces. Take the upwards direction to be positive, so the downwards force is $-5N$ .

$5N - 5N = 0N$

Find the value of the horizontal force by adding forces. Take right to be positive.

$15N -5N=10N$

Therefore the object has a resultant force of $\underline{10N}$ .

Maths; Forces and motion; KS5 Year 12; Force diagrams