Why does high speed collisions like falling cause more damage?

Question

I’m kinda confused, obviously it’s because there is more force involved in the collision compared to a slow speed collision, but why? It’s just the way the universe works, or what?

In: Physics

Answer 1

As you said, it really comes down to force. There is an equation that applies here: Force equals mass multiplied by acceleration, or f=ma

This acceleration variable is related to speed, so that variable in the equation changes depending on the speed at the time of impact. Acceleration is the rate of change of speed (so how much something is speeding up or slowing down). Thinking about this with a car hitting a pole might be simplest. Let’s say that the car hits the pole, and then comes to a stop. Imagine this same situation twice, once with the car going fast, and once with it going slow.

You know, conceptually, that the slow speed will cause less damage. This is because there is less force generated by the impact (remember, force equals mass times acceleration).

This makes sense when you look at the equation, f=ma. First you have force, which is what you are trying to solve for here (That’s what causes the damage, more force equals more damage).

Then you have mass, which will stay the same in this thought experiment, since it’s the same car involved.

The thing that changes here when you change the speed of the crash is acceleration. This is because when the car is going fast, it has a greater amount of speed to lose to get to a stop than that same car would when it was going slower. Rephrased, that means the change in speed is greater, which means the acceleration variable is greater.

With math, it makes sense that when you multiply a constant variable (mass) by another one (acceleration), you get a higher result when you multiply it by the bigger version of that variable. Because of this (since f=ma), you have a greater force when there is a higher acceleration variable. As we’ve established, the acceleration variable is higher when the speed is higher- therefore, you have a greater force generated with a higher speed crash.

That’s the math answer at least. Another, maybe simpler way to think about it is by imagining yourself getting hit by a car. The faster the car, the more you’re going to get hurt- you are trying to “absorb” more acceleration to stop the car with your body. The more acceleration something tries to “absorb,” the more likely the force generated by that will cause something to break.