Impulse

(Triple Only)

Impulse is simply another name for the change in momentum. When something's momentum changes, we can call that change the "impulse". It's measured in the same units as momentum: kilogram metre per second (), or you might see it written as newton seconds (), which is exactly the same thing.

So if a car's momentum changes from to when it crashes, the impulse is . The impulse delivered to the car is equal to the change in its momentum.

Formula:

The Force-Impulse Connection

Here's where it gets really useful. When a force acts on an object for a certain amount of time, it causes the object's momentum to change. The bigger the force, or the longer it acts, the bigger the change in momentum.

This gives us a key force equation.

Formula:

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

• If you decrease the time (), the force () increases

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

Example: a skier of mass is skiing down a mountain at but crashes into a snow drift, coming to a stop. We can work out the force that acts on them if we know how long it takes the skier to come to a stop - in this example lets use :

First, we need to calculate the impulse:

Now we can calculate the force:

All safety features work on the same principle: the momentum change will always remain constant (you have to stop either way), but they can increase the time over which that change happens, which massively reduces the force.

Let's think about a car crash. Your momentum needs to go from a high value to zero - that's fixed. But different scenarios give different forces depending on the time taken:

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

• Time to stop: maybe

• Force: HUGE (potentially fatal)

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

• Time to stop: maybe ( times longer)

• Force: times smaller than Scenario 1 (survivable).

Same change in momentum in scenario B, but because is times bigger, F is times smaller.

How Each Safety Feature Increases Time

Airbags: When your head hits an airbag instead of the hard dashboard or steering wheel, the airbag compresses and deflates gradually. This might take instead of for hitting a hard surface. The airbag increases , so decreases. Same change in momentum (your head has to stop), but much lower force means much less 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 from perhaps to . That increase in time means the force on your chest is smaller. Without this stretch, the seatbelt would cause serious injuries even as it saves your life.

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. As the crumple zone collapses, it takes time - maybe for the car to come to rest, rather than if the car was completely rigid. The crumpling increases dramatically, which reduces the force on passengers by the same factor.

Crash mats in gyms: When a gymnast lands on a thick crash mat, they sink into it. This takes time - maybe instead of landing on a hard floor. The mat increases delta t by , so the impact force is reduced by . This is 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 compared to your skull hitting the road directly. Even though it might only be instead of , that increase in time means less 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. A fall onto concrete might stop you in , but a cushioned surface might extend this to s. That increase in time means less force, turning a potentially serious injury into a minor bump.

The impulse equation and Newton's second law () are actually the same thing, just written differently.

Starting with : We know that

So:

Rearranging:

And since

So and are identical equations.

Newton actually originally wrote his second law in terms of momentum (the impulse form), not in terms of acceleration. The impulse version is more fundamental because it works even when mass changes, whereas assumes mass is constant.