When a (resultant) force is exerted on a body the (resultant) force, the mass of the body and the acceleration caused by the force can be summarised in the equation

F=ma

where f= (resultant) force, m=mass,a=acceleration.

Example

So for example if gravity is pulling down on a body of mass 2kg and is causing it to accelerate at 9.81ms^-2 then we can work out that the force of gravity acting down on the body (what we refer to as its weight) is
2 x 9.81 = 19.62N

When more than one force is acting

If multiple forces are acting on a body along one line (ie we don’t need to worry about the angles between the forces) then each one is causing the body to accelerate at different rates but obviously the body can only have a single rate of acceleration. To understand this problem you need consider the resultant force and resultant acceleration. These are formed by summing all the forces and acceleration respectively. So

where the ‘s are the different forces acting on the body, so gives the resultant force and the ‘s are the different accelerations associated with these forces, so gives the resultant acceleration. Also note that both the forces and accelerations have signs, you must take one direction as positive and the other as negative and give signs accordingly.

Multiple Force Example

Suppose the the body from the above example (of mass 2kg) is again falling under gravity of 19.62 newtons but it is encountering air resistance on 2 newtons against its fall. Find the acceleration of the body.
SO applying the formula (taking downwards as positive)
19.62 – 2 = 2 x a
which gives