Momentum

In this section, we will look at momentum, when it appears and how it affects various situations. To the right, there is an image of a device called ‘Newton’s cradle’ which perfectly demonstrates the effects of momentum and a physics conservation law. If you were to pull back one of the balls on the left and let it go it would collide with the other balls and the vibrations would travel through. This would cause the last ball on the right to swing away from the other balls. This initial collision conserves momentum. When the last ball returns back it collides again with the other balls and the vibrations are passed back along, resulting in the first ball moving outwards. This movement continues due to the conservation of momentum.

Any object which is moving in any direction has momentum. Momentum is the tendency of the object to continue to move in that direction. Momentum is a vector quantity and is measured in kilogram metres per second (kg m/s). It is a measurement used to show how difficult it is to stop something that is moving. The higher the momentum, the more difficult it is to stop that object. The more mass an object has, the more momentum it will have. A good example is a rollercoaster. They have a very large mass but are able to pick up great momentum and accelerate to high speeds. The momentum of a moving object also increases with its speed. As the speed of the rollercoaster increases, its momentum also increases and it would be harder to stop.

You must remember this equation and be able to rearrange it as you will not be provided with it in the exam.

Momentum and acceleration

As the equation shows, momentum is dependent upon the mass of the object and the velocity with which it travels. Velocity is a vector quantity. It has both size and direction. If the object accelerates or decelerates or changes direction, the momentum of that object will also change.

These changes are brought about by the action of resultant forces on the object. Any change in the action of this resultant force causes a change in momentum. The rate of change in momentum of an object is proportional to the size of the resultant force applied to the object. If you were to double the force that is acting on an object, its momentum would also change twice as quickly. The diagram below demonstrates the effect of the thrust force (the sudden push of an engine to accelerate) on the velocity and momentum of the rocket.

The thrust of the motor makes the velocity increase, thus increasing the momentum of the rocket.

To calculate the change in the momentum of any object we use the equation:

This equation can be used to calculate the increase in the momentum of the rocket as follows:

In order to work out the force needed to change the momentum, you use the equation:

Which is the same as:

This equation can be rearranged and present a familiar equation F = ma:

(since this is now the change in momentum over time, which is the same as acceleration)

Then

(since this is now the change in momentum over time, which is the same as acceleration)

Newton’s third law

Newton’s third law states that when two objects interact, they exert forces on each other. The paired forces are equal in size but opposite in direction. This means that the two forces exerted cancel each other with no resultant force occurring. For example, if two cars collide with each other, both cars will exert equal and opposite forces on each other in the collision. The acceleration of the cars in the collision would differ depending upon their mass. A car with a smaller mass would have a much larger acceleration and would be likely to sustain more damage.

Momentum and energy conservation

Now that we have established how momentum works alongside other forces, we can look at how momentum and collisions are connected. To begin with, let’s rearrange the momentum equation to give force x time = increase in momentum. This rearranged equation shows that the longer a larger force is applied to an object, the greater its momentum will be.

This can be illustrated using the example of a collision between two cars. At the time of the collision, the two cars will exert a force onto one another. If the cars are both travelling at a high speed, they will collide with great momentum. The force that is exerted will then act in the opposite direction for the same amount of time. This would mean that the increase in momentum (f x t) would be the same. The increase in momentum of one car would become balanced by the decrease in momentum of the other. This means that the total momentum of both cars would stay unchanged before and after the collision (as long as the friction force is so small as to not affect the collision). This means that we can say the momentum before a collision is the same as the momentum after a collision. In other words, the energy in a collision is conserved as it does not increase or decrease.

Safety features

When a change of momentum occurs in an accident the forces involved can be of such a great magnitude that they cause severe damage to objects or injury to people involved. The relationship between force, change in momentum and time taken is an important consideration for scientists who work to try and find ways to reduce these forces. As shown by the equation:

The larger the change in momentum, the larger the force applied to the object or person. To try and reduce the force, scientists look for ways in which they can reduce the size of the change of momentum or increase the time taken, thus minimising the size of the force transferred to the person.

In a moving car the passenger and car both have momentum. In the case of a collision this means that both will also encounter a change in momentum.  Safety features on cars such as airbags, seatbelts and crumple zones are all designed to try and slow down the change in momentum in the case of a collision. They allow the passenger and car to come to a stop much more gradually than they would without those features in place, reducing the forces involved and reducing the severity of the damage and injuries.

Other safety features such as cushioned surfaces in playgrounds, crash mats for gymnastics, cycle helmets and riding helmets are all designed to also slow down the change of momentum and again reduce the forces involved.