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.
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 equilibrium.
If the resultant force is not zero, a moving object will speed up or slow down - depending on the direction of the resultant force:
Note that the object could also change direction, for example if the resultant force acts at an angle.
Here is the equation that relates acceleration to force and mass:
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.
The triangle diagram may help you to rearrange the equation so you can calculate acceleration.
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:
When you are doing this kind of problem, always work in one dimension at a time.