What are the key learning points about force and Newton's laws?
Forces arise between objects, the forces on these objects are equal and opposite.
Friction is a force that always opposes motion.
Force is measured in newtons (N).
A force acting in one direction can be given a positive value and one acting in the opposite direction can be given a negative value, the resultant force of two one-dimensional forces can be calculated by combining these values.
Newton’s first law states that, in the absence of unbalanced forces, an object will continue to move in a straight line at constant speed (i.e. move with constant The rate of change of displacement. The distance travelled in one second in a specified direction. Measured in m/s.).
Newton’s second law states that a resultant force will cause an object to The rate of change of velocity. It is measured in metres per second squared (m/s²). Acceleration = change of velocity ÷ time taken. and that the acceleration is proportional to the size of the resultant force.
resultant force = The amount of matter an object contains. Mass is measured in kilograms (kg) or grams (g). × acceleration.
What are forces?
A force is a push or a pull.
Contact forces arise between two objects which are in contact.
Non-contact forces act between two objects which are not in contact.
What are contact forces?
Contact forces are forces that act between two objects which are physically touching each other.
What is an example of a contact force?
Friction is a good example of a contact force.
Two objects sliding past each other experience friction forces.
For example, a box sliding down a slope.
Remember that friction is a force that always opposes motion.
It acts in the opposite direction to the one in which the box is moving.
What are non-contact forces?
Non-contact A push or a pull. The unit of force is the newton (N). are forces that act between two objects that are not physically touching each other.
What is an example of a non-contact force?
A good example is a magnetic force.
A Able to be magnetised or attracted to a magnet. force is experienced by any magnetic material in a A region around a magnet or around a wire carrying a current, where a magnetic force is experienced..
Opposite magnetic poles (N - S or S - N) Objects that tend to move together because of a force between them attract each other. each other – but do not need to be in contact.
Like magnetic poles (N - N or S - S) Objects that tend to push apart because of a force between them repel each other. each other – but do not need to be in contact.
Key points
- Force is measured in newtons N.
- Force is a vector quantity - direction is important as well as size.
- A force acting in one direction is given a positive value.
- A force acting in the opposite direction is given a negative value.
When forces act between two objects, both objects experience an equal size force, but in opposite directions.
This is Newton's third law of motion.
What are friction and air resistance?
Friction is a force that exists between two surfaces that are in contact.
Friction can be useful in some circumstances and a nuisance in others.
The friction between our shoes and the ground helps us to walk.
Whenever we try to walk on ice where the friction is reduced, it is much more difficult.
Friction between the parts in a car engine is a nuisance as it causes the engine to heat up and causes the metal parts to wear away.
What are ways of reducing friction?
To make something move more smoothly, for example by adding oil or grease to part of a machine. surfaces by adding a layer of oil or grease to separate them.
Using an air stream so surfaces are no longer in contact with eachother.
Make surfaces smoother by removing jagged pieces that catch each other.
Use ball bearings which decreases the contact area between surfaces.
Air resistance
Air resistance is a type of friction which bodies that are moving through the air experience.
It also acts to oppose motion.
Air resistance depends on the area of the body and the speed at which it is moving.
Air resistance can be sometimes useful, e.g. parachuting.
WATCH: A demonstration of friction
This short video gives a demonstration of friction.
How to carry out calculations involving forces
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 is Newton’s first law?
Key fact
- Newton’s First Law 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
Balanced forces
This simply means that balanced forces, acting on the same object, will have no effect on the motion of an object.
In practice this means:
it could be Not moving or at rest.
or it could be moving at constant speed in a straight line (constant The rate of change of displacement. The distance travelled in one second in a specified direction. Measured in m/s.).
What is an example of balanced forces?
The forces acting on this car are balanced.
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
If the forces on an object are balanced (no resultant force) then:
if it is at rest, it stays at rest;
if it is moving, it keeps on moving at a constant speed in a straight line (constant The rate of change of displacement. The distance travelled in one second in a specified direction. Measured in m/s.)
How to investigate experimentally Newton’s second law
This practical uses light gates and a data logger to investigate resultant force and acceleration.
Key fact
- 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. is the single A push or a pull. The unit of force is the newton (N). acting on the object when all the individual forces have been combined.
What are the steps involved in carrying out this investigation?
- A force that opposes or prevents movement. When work is done against friction, kinetic energy is converted into heat energy. is compensated by having the runway tilted slightly so that the trolley moves at constant speed.
- Attach a length of card to the trolley. Measure the length of card with a 30 cm ruler.
- Set up light gates and data logging software to measure The rate of change of velocity. It is measured in metres per second squared (m/s²). Acceleration = change of velocity ÷ time taken. from A to B. When prompted, type the length of card in cm.
- Put a 100g masses on to the mass hanger. Place 6 other 100g masses on the trolley.
- The 100g mass on the hanger acts as a resultant force of 1N accelerating the trolley along the runway. Record the force F in a suitable table.
- Release the trolley and allow the card to pass through light gates A and B. Record the acceleration.
- Repeat twice and average the acceleration.
- Move a 100g mass from the trolley to the hanger. This ensures that the mass being accelerated remains constant. Record F and repeat 6 and 7 above. Repeat for each mass in turn.
How to record the results
It is important to record results in a suitable table, like the one below:
| Force / N | Run 1 acceleration / m/s2 | Run 2 acceleration / m/s2 | Run 3 acceleration / m/s2 | Mean acceleration / m/s2 |
|---|---|---|---|---|
Graph
Plot a graph of 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. F in N on the y-axis against acceleration a in m/s2 on the x-axis. Draw the line of best fit.
The graph is a straight line through the origin.
This tells us that resultant force, F, and acceleration, a, are When one variable is zero so is the other. As one variable increases the other does at the same rate. When 𝒚 is plotted against 𝒙 this produces a straight-line graph through the origin..
If you double the resultant force acting on an object, you double its The rate of change of velocity. It is measured in metres per second squared (m/s²). Acceleration = change of velocity ÷ time taken..
What safety measures should be followed?
| Hazard | Consequence | Control measures |
|---|---|---|
| Masses and hanger falling to floor | Objects falling on feet - bruise/fracture | Use relatively small masses and step back after releasing masses. Place bench stools as a cordon beneath the accelerating masses to prevent feet being placed beneath them. |
How to investigate mass and acceleration
A second experiment can be carried out using the apparatus above, to investigate how the The rate of change of velocity. It is measured in metres per second squared (m/s²). Acceleration = change of velocity ÷ time taken. of an object depends on its mass, if the resultant force remains constant.
Use an accelerating force of 5 N and keep this constant.
Record acceleration as additional 0.5 kg masses are added to the trolley.
Graph
Plot a graph of mass m in kg on the y-axis against acceleration a in m/s2 on the x-axis.
Draw a smooth curve through the points.
The graph is not a straight line through the origin – mass and acceleration are notWhen one variable is zero so is the other. As one variable increases the other does at the same rate. When 𝒚 is plotted against 𝒙 this produces a straight-line graph through the origin..
Plot a second graph of 1/mass in 1/kg on the y-axis against acceleration a in m/s2 on the x-axis.
Draw the line of best fit.
This graph is a straight line through the origin.
Acceleration is directionally proportional to 1/m.
We say that mass and acceleration are Two variables are said to be inversely proportional when one increases by a factor of two (doubles) the other decreases by a factor of two (halves)..
If you double the mass, you half the acceleration.
Key facts
When the forces acting on an object do not balance, 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. causes the object to The rate of change of velocity. It is measured in metres per second squared (m/s²). Acceleration = change of velocity ÷ time taken. in the direction of the resultant force.
Acceleration is When one variable is zero so is the other. As one variable increases the other does at the same rate. When 𝒚 is plotted against 𝒙 this produces a straight-line graph through the origin. to resultant force if the mass remains constant.
Acceleration is Two variables are said to be inversely proportional when one increases by a factor of two (doubles) the other decreases by a factor of two (halves). to mass if the resultant force remains constant.
In other words, a resultant force on a body will cause it to change its The rate of change of displacement. The distance travelled in one second in a specified direction. Measured in m/s..
This simply means that unbalanced forces will cause:
acceleration;
deceleration;
a change in direction.
What is Newton's second law?
Newton’s second law follows from the results of the above experiments.
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 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
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.
Question
In a theme park, one of the rides has a motor that can deliver a forward force to an empty passenger car.
A force of A force that opposes or prevents movement. When work is done against friction, kinetic energy is converted into heat energy. of 400 N acts on the car which has a mass of 500 kg and it accelerates at a rate of 2.0 m/s2.
Calculate the forward force delivered by the motor.
Answer
F = ma
Resultant force = F - 400 N
a = 2.0 m/s2
m = 500 kg
F - 400 N = 500 kg x 2.0 m/s2
F = 1000 N + 400 N
F = 1400 N
The forward force delivered by the motor is 1400 N.
How much do you know about force and Newton's laws?
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