# Calculating unbalanced forces

An object may have several different forces acting on it, which can have different strengths and directions. But they can be added together to give the resultant force. This is a single force that has the same effect on the object as all the individual forces acting together.

## Resultant force and acceleration

If the resultant force is zero, a moving object will stay at the same speed. If there is no resultant force then a system is said to be in .

If the resultant force is not zero, a moving object will speed up or slow down - depending on the direction of the resultant force:

• it will speed up if the resultant force is in the same direction as the object is moving
• it will slow down if the resultant force is in the opposite direction

Note that the object could also change direction, for example if the resultant force acts at an angle.

## Calculating acceleration

Here is the equation that relates acceleration to force and mass:

force = mass × acceleration

force is measured in newtons, N

mass is measured in kilograms, kg

acceleration is measured in metres per second squared, m/s2.

For example, the force needed to accelerate a 10 kg mass by 5 m/s2 is

10 × 5 = 50 N

The same force could accelerate a 1 kg mass by 50 m/s2 or a 100 kg mass by 0.5 m/s2.

You should see that it takes more force to accelerate a larger mass.

Triangle showing force equals mass multiplied by acceleration

The triangle diagram may help you to rearrange the equation so you can calculate acceleration.

Question

An aircraft of mass of 1200 kg starts from rest and accelerates along a straight horizontal runway. The aircraft engine produces a constant thrust of 3400 N. A constant frictional force of 400 N acts on the aircraft.

Calculate the acceleration of the aircraft.

m = 1200 kg

Engine = 3400 N

Friction = 400 N

F = (3400 - 400) = 3000 N

F = ma

3000 = 1200 × a

a = 2.5 ms-2

In some situations, forces on an object act in more than one dimension. For example, for an aircraft in flight there are at least four forces acting:

• the forces of the engine (horizontal force)
• air resistance (horizontal force)
• the force of gravity (vertical force)
• the up-thrust from the wings (vertical force)

When you are doing this kind of problem, always work in one dimension at a time.