# Newtons Laws of Motion

## First Law of Motion

An object will remain at rest unless acted upon by a resultant force. A moving object will remain at a constant velocity unless acted upon by a resultant force.

Sir Isaac Newton was one of the greatest scientists to study forces and motion. He came up with three laws of motion.

In his first law, he describes something we all know anyway. It might sound confusing but it is really just common-sense.

Objects do not move unless you push or pull them, once you get an object moving you need another force to speed it up, slow it down or to make it turn.

If you have ever ridden a bike, you already know all about Newton’s First Law of Motion.

Peddle faster to increase speed, (you apply a force).

Pull the brakes to slow down, ( you apply a force).

Turn the handlebars to corner, (you apply a force).

**What is a resultant force?**

When you are riding a bike there are lots of different forces all acting on you and the bike at the same time. There is gravity, pulling you down, there is the friction between the tyre and the road, there is the air resistance as you cycle along, there is the force from the pedals as you cycle.

The resultant force is the overall effect these have on you and the bike, the various forces act as if they have been combined into one single force.

Example:

You produce a forward force from the pedals of 50 N, the friction from the road causes a 20 N force backwards. 50 N - 20 N gives a 30 N resultant force forwards.

**Effects of a Resultant Force on Movement**

Positive resultant force - the object will accelerate in the direction of the force and speed up.

Negative resultant force - the object will decelerate and slow down.

The resultant force is at an angle to the direction of movement - the object with change direction and moves in the direction of the force - it turns.

If the forces all balance each other, then the resultant force is zero. In this situation, the object moves along at the same speed and in the same direction.

In the example above there was a 30 N forward resultant force, how would this affect the motion of the object?

Answer: It would accelerate forwards, it would be getting faster.

One of the most common misunderstandings about Newton’s First Law is this ;

If the resultant force is zero, the object is not moving. **WRONG**

Zero resultant force means zero change. So if the object was stationary it stays that way, no change. If the object was moving at 3 m/s north, it stays moving at 3 m/s north, no change.

## Inertia

Inertia is the tendency for an object to the resist any change in its movement. The more massive the object the greater the inertia.

It is defined as the ratio of the force applied to an object to the acceleration of the object.

Heavy objects require more force than lighter objects to get them to move. Inertia also means that it’s harder to get large objects to speed up, slow down, and turn once they are moving.

Did you know it can take an oil tanker up to 25 km (15 miles) to stop? This is due to the very large inertial mass of the ship. The braking force from the engines has to be applied for a long time to have any effect on the motion of the ship.

The increased inertia of an overloaded vehicle means the brakes can’t produce enough force quick enough to stop it safely in an emergency. The high mass produces a high level of inertia, so the vehicle takes too long to stop.

## Second Law of Motion

Newton recognised that the acceleration of an object depended on two factors.

- The mass of the object
- The force applied to the object. (or the resultant force to be accurate).

He summarised this relationship in the equation:

_Force = mass x acceleration or__ __F = m a _

If we rearrange this to; *a = F / m*, we can see that acceleration is proportional to the force applied, but inversely proportional to the mass of the object.

Which means; larger heavier objects accelerate more slowly for the same force, and a bigger force makes an object accelerate quicker.

Worked Example 1

Compare the force needed to make a car of 1500 kg accelerate at 3 m/s/s with a car of 2000 kg accelerating at the same rate.

Use the formula;_ F = ma_

1500kg car F = 1500 x 3 = 4500 N

2000kg car F = 2000 x 3 = 6000 N

Worked Example 2

A bike has a mass of 30 kg and its rider 75 kg. The friction and the air resistance produce a force of - 150 N. The force from the pedals products as a force of + 450 N.

**What is the acceleration of the bike and its rider?**

Mass - combine the 2 masses - 30 + 75 = 105 kg

Work out the resultant force - 150 + 450 = 300 N

Use the formula: *a = F / m*

𝑎 = 300 / 105

𝑎 = 2.86 m/s/s

**What effect does this have on the rider and the bike?**

Answer: They are increasing their speed in a forwards direction.

## Investigating Second Law of Motion

Using the experimental set-up for measuring speed we can also investigate Newton’s Second law of motion.

The most reliable and accurate method would be to make use of either light gates or sonar senses to monitor the motion of the trolley along the ramp or trackway. It can be achieved with a stopwatch too. This is the least accurate method to use.

The procedure is the same whichever method is chosen.

When carrying out any investigation it is important to only have one input variable and one outcome variable. Other variable should remain the same (control variables).

The effect of the mass of an object on its acceleration can be achieved by placing weights onto the trolley. The mass on the mass holder that provides the force must remain unchanged.

The effect of the force can be investigated by keeping the mass of the trolley unchanged and increasing the number of mass on the mass holder.

**Safety:** it is important in any investigation to consider safety. In this experiment, the hazards are the masses falling and pulling the trolley. They could land on someone’s foot etc. The mass of the moving trolley and how you stop it before it is pulled off the lab bench. To limit the risk of injury the number of masses used is normally kept to a safe limit.

Key points to recall about this experiment.

- There are two variables to investigate, but they must be investigated as separate parts of the experiment. DO NOT change the mass and the force at the same time. This would not be a fair test.
- Safety; moving heavy objects are a hazard, the best way to reduce the risk is to limit the masses used.

## Third Law of Motion

For every action, there is an equal, but opposite reaction.

As the man steps out of the boat, the action of him moving forwards is balanced by an equal but opposite reaction from the boat, which moves backwards. Both experience the same force but in opposite directions.

The idea that the reaction is __equal __does not mean that the two objects have to move the same distance. The mass of the two objects affects the degree of the action and reactions.

If you step off a boat with a mass about the same as your own mass, you and the boat will move roughly the same amount. If on the other hand, you step off a large ferry, you may move a meter or more but the boat will hardly move at all. Importantly, however, it does move.

Making the Earth move, dropping an apple.

If you accidentally dropped your phone it would fall due to gravity.

For an average phone that’s a force of about 13 N.

The earth, however, has to have a reaction to this is in the opposite direction. It has to move up towards the phone.

So why don’t we see the earth move? The force is equal on both, 13N, the phone has a mass of about 0.13 Kg. The earth has a mass of 5.98 x 10^{24 }Kg. The 13 N force doesn’t produce a movement we would see, but there is a reaction.

**Collisions**

A collision is when two object hit each other, or crash into each other. When this happens there is an interaction between the two objects.

Each object experiences an equal but opposite force. The effect of that force on each object depends on their masses. The greater the mass the less the impact the force has on the motion on the object.

Remember Newton’s Second Law: *a = F /m*

In a collison F is the same on each object, but the acceleration will depend upon the object’s mass.

Examples

**Kicking a ball**

When the boot collides with the ball, they both experience the same force. The ball is much lighter than the player so the acceleration is greater too. We see the ball move.

The same force applied to the player has a much smaller acceleration effect. It is also in the opposite direction so the swing of the leg decelerates slightly.

**Car crash**

If a car runs into the back of a stationary car, both cars experience the same force but in opposite directions. The moving car experiences a backwards force and slows down, the other car experiences a forwards force and so speeds up.

In all these situations the combined velocities of the objects before and after the collisions remains the same. Therefore, **the momentum is also conserved**.

- If a friction between a ball and the ground is equal to 5 N and the ball is kicked forwards with a force of 10 N, what will happen to the ball and why?
- accelerate

Explanation:*The ball will accelerate in the forward direction. This is because there is a resultant force of 5 N acting on the ball. [extension: this is only if the 5N is sufficient to overcome the inertia of the ball.]* - A lorry of mass 20,000 Kg accelerated at 1.5 m/s/s, what force is required?
- Your answer should include: 30000 / 30000N

Explanation:*F = ma F = 20,000 x 1.5 = 30,000 N* - Explain what happens when a stationary snooker ball is hit by a moving one, assume they have equal masses.
- Your answer should include: forwards / slow down / opposite force / acceleration / magnitude / direction

Explanation:*The stationary ball will start to move forwards and the moving one will slow down. Both balls experience an equal but opposite force. As their masses are equal their acceleration will be equal in magnitude but opposite in direction.*