Changes in Momentum (GCSE Physics)

Changes in Momentum

Forces and Momentum

• Forces change the speed or direction of moving objects. When objects are moving, forces can act on them. These forces can change the speed of an object, or change the direction in which the object is moving. In this way, forces can change the velocity of an object.
• Forces can therefore change momentum. Since forces can change the velocity of an object, this means they must also be able to change the momentum of an object. This is because momentum = mass x velocity, so if the velocity changes, then the momentum also changes.

Combining Equations

For exams, you need to be able to show that force is equal to the rate of change of momentum. We can do this in the following way.

1. We need to use two equations.
For this proof, we will be combing two equations we have seem previously.

F = m × a
a = (v-u) / t

2. Rearrange both equations.
Now that we have both equations, we need to rearrange them to get ‘a =’.

F = m × a
a = F / m
a = (v-u) / t

3. Make both equations equal.
We can now equal both the equations to each other and rearrange to get ‘F =’.

a = F / m
a = (v-u) / t
F/m = (v-u) / t
F = m(v-u) / t
Since (v-u) = ∆v
F = m∆v / ∆ t
F /∆ t = m∆v

In other words, the impulse is equal to the change in momentum. The impulse is the product of average force and and time of a contact in a collision.

Safety Features and Momentum

In everyday life, a lot of safety features are designed based on momentum. To explain this, we can look at the equation we just learnt:

F = m∆v / ∆ t

We can decrease the force on an object by increasing the time taken for the change in momentum to happen, as demonstrated below:

F = m∆v / ∆ t

Example 1. When the momentum is 30 kg m/s and the time taken is 3 seconds:

F = 30 / 3
F = 10 N

Example 2. When the momentum is 30 kg m/s and the time taken is 6 seconds:

F = 30 / 6
F = 5 N

As you can see, when the time increases from 3 seconds to 6 seconds, the force experienced by the object will decreases significantly. In other words, as the rate of change of momentum decreases, the force experienced by the object will also decrease.

The following safety measures use the principle of decreasing the rate of change of momentum in order to decrease the force experienced by objects:

1. Air Bags
   
   Air bags will inflate in the event of a car crash. The passenger will naturally move forwards due to impact, but instead of hitting the hard dashboard, they will hit the air bag. The air bag will absorb some of the impact, slowing down the passenger considerably. By increasing the time taken for the passenger to move, the air bag will decrease the rate of change of momentum, therefore decreasing the force on the passenger’s body.
2. Seat Belts
   
   Seat belts are worn as a safety measure by all passengers in a car. These are often stretchy, allowing for the passenger to move slightly before coming to a stop. In this way, seat belts will increasing the time taken to come to a stop, and hence decrease the rate of change of momentum and therefore decrease the force experienced by the passenger.
3. Gymnasium Crash Mats
   
   Crash mats are commonly used by gymnasts to reduce the force of impact. Since these mats are compressible, a gymnast will ‘sink’ into the mat slightly and take a longer time to come to a complete stop. Therefore they increase the time taken to come to a stop, and therefore decrease the rate of change of momentum and therefore a decrease in the force experienced when the gymnast lands on the floor.
4. Cycle Helmets

   Inside a cycle helmet, there is usually a layer of foam. This foam acts very much in the same way as crash mats; it is a compressible layer which reduces the force of impact by increasing the time taken to come to a stop. By doing so, we can reduce the chances of any head injuries.

5. Cushioned Surfaces

   Many playgrounds often have slightly softer, cushioned surfaces. They are compressible, so if a child falls over, they will take longer to completely stop moving. The surface increases the time taken to come to a stop. This reduces the chance of the child injuring themselves.

Linking force, mass, velocity and acceleration

In this chapter, we have seen various relationships to do with force, mass, velocity and acceleration.

We have already linked force, mass and velocity through the following relationship:

F = m∆v / ∆ t

We can now link acceleration to this relationship, to gain an equation we have seen before:

Since a = ∆v / t
So F = ma

As you can see, this means that the equations to do with force, mass, velocity and acceleration are linked. In exams you may be given questions where you are expected to use more than one equation, or rearrange equations to find a missing value.