Resultant force
If the push and the pull are not the same size, the forces are not balanced, and a resultant force acts on the object.
What happens when a resultant force acts on an object?
Newton’s second law tells us that when a resultant force acts on an object it accelerates. That means:
- it speeds up or slows down, and/or
- it changes direction.
The relationship between the The single force that could replace all the forces acting on an object, found by adding these together. If all the forces are balanced, the resultant force is zero., the The amount of matter an object contains. Mass is measured in kilograms (kg) or grams (g). of the object and the object’s The rate of change in speed (or velocity) is measured in metres per second squared. Acceleration = change of velocity ÷ time taken. is:
Resultant force = mass x acceleration
F = ma
F = resultant force in N
m = mass in kg
a = acceleration on m/s2
| \({F} = {ma}\) | \({F} = {m}\times{a}\) |
| \({m} =\frac{\text{F}}{\text{a}}\) | \({m} = {F} \div {a}\) |
| \({a} = \frac{\text{F}}{\text{m}}\) | \({a} = {F} \div {m}\) |
| \({F} = {ma}\) |
| \({F} = {m}\times{a}\) |
| \({m} =\frac{\text{F}}{\text{a}}\) |
| \({m} = {F} \div {a}\) |
| \({a} = \frac{\text{F}}{\text{m}}\) |
| \({a} = {F} \div {m}\) |
The newton N
The unit of force is the newton N.
One newton is the resultant force that gives a mass of 1 kg an acceleration of 1 m/s2 in the direction of the force.
1 N = 1 kg x 1 m/s2
Example
A box of mass 1.2 kg accelerates at 2 m/s2.
What is the resultant force acting on the box?
Answer
F = ma.
F = resultant force in N.
m = 1.2 kg.
a = 2 m/s2.
F = 1.2 x 2 = 2.4 N.
The resultant force acting on the box is 2.4 N.
Question
A car has a mass of 1000 kg and a resultant force of 5000 N acts on it.
What is the acceleration of the car?
a = \(\frac{\text{F}}{\text{m}}\)
F = 5000 N
m = 1000 kg
a = \(\frac{\text{5000 N}}{\text{1000 kg}}\)
a = 5 m/s2
The acceleration of the car is 5 m/s2
In the example below two forces act on the car.
To calculate the acceleration, the resultant of the forces must first be found.
a = \(\frac{\text{F}}{\text{m}}\)
The resultant force F = 4000 N - 1000 N
= 3000 N
F = 3000 N
m = 1000 kg
a = \(\frac{\text{3000 N}}{\text{1000 kg}}\)
a = 3 m/s2
The car accelerates because the car is moving in the same direction as the resultant force.
Now look at a second example. The forward force remains at 4000 N.
a = \(\frac{\text{F}}{\text{m}}\)
The resultant force F = 4000 N - 7000 N = -3000 N
The resultant force is negative because it acts in the opposite direction to which the car is moving.
F = -3000 N
m = 1000 kg
a = \(\frac{\text{-3000 N}}{\text{1000 kg}}\)
a = -3 m/s2
The car now has an acceleration of -3 m/s2 or a deceleration of 3 m/s2.
This means it will slow down.
