What are the key learning points about this topic?
To distinguish between balanced and unbalanced forces.
To calculate resultant force.
To calculate the acceleration of an object.
What are forces?
A force is a push or a pull.
Contact forces arise between two objects which are in contact.
Friction is an example of a contact force.
Non-contact forces act between two objects which are not in contact.
The force of gravity and magnetic force are examples of non-contact forces.
What is a resultant force?
The resultant A push or a pull. The unit of force is the newton (N). is the single force that has the same effect as two or more forces acting together.
What happens when two forces act in the same direction?
Two forces that act in the same direction produce a resultant force that is larger than either individual force.
You can easily calculate the resultant force of two forces that act in a straight line in the same direction by adding their sizes together.
What is an example of two forces acting in the same direction?
Two forces, 3 N and 2 N, act to the right.
Calculate the resultant force.
Resultant force F = 3 N + 2 N = 5 N to the right.
The resultant force is 5 N to the right.
What happens when two forces act in opposite directions?
Two forces that act in opposite directions produce a 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. that is smaller than either individual force.
To find the resultant force subtract the magnitude of the smaller force from the magnitude of the larger force.
The direction of the resultant force is in the same direction as the larger force.
What is an example of two forces acting in opposite directions?
A force of 5 N acts to the right, and a force of 3 N act to the left.
Calculate the resultant force.
Resultant force F
Resultant force F = 5 N - 3 N = 2 N to the right.
The resultant force is 2 N to the right.
What are balanced forces?
If the push and the pull are the same size, then no resultant force acts on the object and the forces are said to be balanced.
Resultant force = 5000 N - 5000 N = 0.
The forces are balanced.
What is Newton's first law?
Key fact
Newton’s first law of motion states that a body will remain at rest or continue to move at constant speed in a straight line, unless a resultant force acts on it.
Another way of saying this is:
If the forces acting on an object are balanced
- it stays at rest if it is already at rest, or
- it keeps moving at constant speed in a straight line if it is already moving at constant speed in a straight line.
Look again at this example:
The thrust from the engine is equal and opposite to the drag caused by air resistance and A force that opposes or prevents movement. When work is done against friction, kinetic energy is converted into heat energy. between the road and car tyres.
There is no resultant (or net) force as the forces add up to zero.
The car will continue to travel forward with a speed of 20 m/s in a straight line.
Another example are the forces acting on this car.
The upward force equals the downward force and they both act on the car.
The car remains at rest.
It does not move upwards or downwards.
Balanced forces have no effect on an object.
If it is at rest, it remains at rest.
If it is moving at constant speed in a straight line, it continues to move at the same speed in the same straight line.
Summary
Balanced forces have no effect on an object.
If it is at rest, it stays at rest.
if it is moving at a constant speed in a straight line, it continues to move at the same speed in the same straight line.
What is Newton's second law?
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 of velocity. It is measured in metres per second squared (m/s²). Acceleration = change of velocity ÷ time taken. is:
Resultant force F = mass m x acceleration a
F = ma
F = resultant force in newton N
m = mass in kg
a = acceleration on m/s2
| \({F} = {ma}\) | \({F} = {m}\times{a}\) |
|---|---|
| \({m} =\frac{\text{F}}{\text{a}}\) | \({m} = {F} \div {a}\) |
| \({a} = \frac{\text{F}}{\text{m}}\) | \({a} = {F} \div {m}\) |
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?
Answer
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
Key fact
- When using the equation F = ma it is important to remember that F is the resultant force acting on the object.
Example
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
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.
It is moving in the opposite direction to the resultant force and slows down.
Question
A car has a mass of 1200 kg, and an engine that can deliver a force of 6000 N.
Find the acceleration of the car.
Answer
a = \(\frac{\text{F}}{\text{m}}\)
F = 6000 N
m = 1200 kg
a = \(\frac{\text{6000~N}}{\text{1200~kg}}\)
a = 5 m/s2
The acceleration of the car is 5 m/s2.
Question
Find the resultant force developed by a speed boat engine, if the boat has a mass of 300 kg and can accelerate at a rate of 1.5 m/s2.
Answer
F = ma
a = 1.5 m/s2
m = 300 kg
F = 300 kg x 1.5 m/s2.
F = 450 N
The resultant force developed by the speed boat engine is 450 N.
Summary
When forces on an object are balanced;
- the object will move at a steady speed in a straight line, or
- remain at rest.
The resultant force is the single force that has the same effect as two or more forces acting together.
The resultant of two or more forces that act in the same direction is found by adding their sizes together.
The resultant of two forces that act in the opposite direction is found by subtracting their sizes.
Newton’s second law tells us that when a resultant force acts on an object it accelerates. That means a resultant force makes an object:
- speed up or slow down, and/or
- change direction.
Resultant force = mass × acceleration or F = ma.
If the resultant force acting on an object is in the same direction as it is moving, it speeds up or accelerates.
If the resultant force acting on an object is in the opposite direction to which it is moving it slows down or decelerates. Eventually it will come to rest.
How much do you know about resultant force and acceleration?
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