Change in Momentum

(Triple Only)

When an object has a change in momentum, it is caused by a force acting on the object for a period of time. The bigger the force, or the longer it acts, the bigger the change in momentum.

We can combine Newton's Second Law () and the acceleration equation () to give us an equation about force and change in momentum:

Formula:

This equation means that for the same change in momentum:

• If you increase the time (), the force applied () decreases

This is the entire principle behind safety features in vehicles and sports equipment.

Example: If a skier of mass is skiing down a mountain at and crashes into a snow drift, coming to a stop, we can work out the force that acts on their head:

Lets say they come to rest over seconds.

But if it took them seconds to stop as they used a crash helmet.

From the maths, we can see that for the same change in momentum, using the helmet increases the time taken to come to rest, significantly reducing the force acting on them.

All safety features work on the same principle: increasing the time over which a collision occurs to significantly reduce the impact force.

Let's think about a car crash. Your momentum changes from a very high value, due to the speed you were travelling at, to zero (when stopped). Your change in momentum is a fixed value; however, if we can change the time over which this change occurs, we can change the force acting.

Scenario A: You hit a solid concrete wall with no airbag

• Time to come to a stop: around

• Force: very large, resulting in multiple serious injuries

Scenario B: You hit a concrete wall, but your airbag deploys

• Time to stop: increased to around ( times longer than without the airbag)

• Force: times smaller than in scenario 1.

How Each Safety Feature Increases Time

Cars include a number of safety features that make use of increasing the time taken for the same change in momentum, to reduce the force acting, as illustrated below:

Airbags: When your head hits an airbag instead of a hard dashboard or steering wheel, it increases the time it takes for you to come to a complete stop, as it will take time for the airbag to compress when your head hits it. The airbag increases the , for the same change in momentum, so the decreases. This results in much lower damage to your skull and brain.

Seatbelts: Modern seatbelts are designed to stretch slightly during a crash. They don't stretch loads, but even a small amount of stretch can increase the time over which you decelerate. If a seatbelt can increase your time to stop from say to , this increase in time means the force on your chest will be smaller for the same change in momentum. Without this stretch, the seatbelt would cause serious injuries.

Crumple zones: These are sections at the front and rear of a car designed to crumple and deform in a controlled way during a crash. If there were no crumple zone when the car hits a wall, it would stop quickly. With the crumple zone, as it takes time for the car to collapse, it would take longer to come to a rest. The crumple zone increases the , for the same change in momentum, which reduces the force on the passengers significantly.

Other scenarios which use increased time to decrease force include:

Crash mats in gyms: When a gymnast lands on a thick crash mat, they sink into it, increasing the time it takes to come to a complete stop. This increase in time can make the difference between a safe landing and broken bones.

Cycle helmets: The foam inside a helmet compresses when you hit your head. This compression takes time, increasing the time your skull takes to come to rest compared to hitting the road directly, thereby decreasing the force on your skull.

Cushioned playground surfaces: Soft rubber surfaces or bark chippings compress when a child falls on them, increasing the time it takes for them to stop. This turns a potentially serious injury into a minor bump.