# Is it viable to talk about physical impacts in terms of force instead of energy?

Like university researchers measuring the force of Ricky Hattons punch with a special bag, or when programs talk about the force of crashes and ballistic impacts like shells and so on.

But force is the mass x the acceleration. That indicates how strong something had to be to accelerate that mass at that rate, but not how hard that mass will impact.

The acceleration doesn't matter at all in an impact, right? A car hitting you at 100 mph does the same amount of damage if it took five minutes to reach that speed as it did if it took several seconds. So, if force is mass x acceleration, it doesn't make sense to measure the impact in terms of force, only what the car had to have in order to accelerate like that.

And then, is impact force an existing term different from the normal term force? What do very descriptive things like pounds per square inch come under? Kinetic energy describes the magnitude of the event, but then these compare the impact to weight over a certain area.

Cyosis
Homework Helper
Acceleration isn't only going from a certain speed to a higher speed. Deceleration is acceleration in physics as well. If you were to punch someone in the face your hand would reach that person's face at a certain velocity and then begin to decelerate. After the impact, his face will compress a bit while your hand is slowing down until it is at rest. It is this deceleration that causes the force.

Example:
When you hit a punching bag, the bag compresses quite a bit and the deceleration is relatively low, therefore the force on your hand is relatively low. In other words your hand doesn't hurt. Now replace this punching bag with a slab of concrete and hit it again at the same speed. The concrete will not give way nearly as much as the punching bag did so the deceleration is far greater. The result, a painful hand. Note that it doesn't matter how fast your hand reached the velocity with which you strike the bag/slab. All that matters is how fast your hand reaches zero after you landed the punch.

This is also the reason why car manufacturers implement crush zones in their car's design. The crush zone increases the time for you to go from impact speed to zero speed. As a result your deceleration is lowered therefore the force is lowered and your chances of survival increase.

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So, it's deceleration that counts in terms of what's being hit?

How would that be expressed (instead of mass x acceleration), or would it be the same?

russ_watters
Mentor
It is still f=ma. Deceleration is acceleration in a different direction.

Cyosis
Homework Helper
Deceleration really just is acceleration in a physical sense, that is the rate at which an object's speed changes. Lets do a few numerical examples, ignoring all friction.

A car of 2000kg starts at rest and accelerates at a constant rate to a speed of 100km/h=27.8m/s in 10 seconds. Then the acceleration is given by 27.8/10=2.78m/s^2 and the force needed for such an acceleration,F=ma=2000*2.78=5560N. Now the car hits a wall with 100km/h and after 20ms it comes to rest. The average acceleration now is (0-27.8)/(0.02)=-1390m/s^2 (minus sign, because it is slowing down). The force imparted by the wall on the car (the force it takes to stop the car in 20 ms) is F=ma=2000*1390=27.8*10^5N. That's quite a difference!

I've often explained to people (or tried to, anyway) that since the force of impact is due to the magnitude of the acceleration, it can be very large for either of two reasons. The acceleration (or deceleration, as pointed out previously) is the ratio of change in velocity to change in time, so you can have a large acceleration either by having a very large change in velocity (as in high-speed crash) or very small change in time (falling over and having your head hit a solid object).

This is the reason crash helmets work. The layer of foam gives your head (and the brain it contains) a couple of milliseconds to decelerate from initial velocity to zero, rather than the virtually instantaneous change that occurs if your head hits something hard and immovable.

Still, if you have two identical cars hitting identical walls at different speeds, the one with the higher speed will have the greater kinetic energy, and will then produce the most force.

Cyosis
Homework Helper
Your kinetic energy-force connection isn't very accurate. If two identical cars hit the wall, one with speed 100km/h the other with 200km/h. Both are stopped after 20 ms. Then the deceleration of the car going with 200km/h will be twice as high, thus the wall imparts a force on that car that is twice as high as well (all with respect to the 100km/h car).

Your kinetic energy-force connection isn't very accurate. If two identical cars hit the wall, one with speed 100km/h the other with 200km/h. Both are stopped after 20 ms. Then the deceleration of the car going with 200km/h will be twice as high, thus the wall imparts a force on that car that is twice as high as well (all with respect to the 100km/h car).
Exactly so - the time to go from initial speed to zero is also needed to talk about the force imparted.

What you (Researcher X) might be thinking about is called the average impulse, which is force times the time over which it's imparted. It has units of momentum, however, not of energy.

This is more tricky than it first appears, you can use both energy or forces to describe a collision.

In real impacts as bits fly off the car not all of the energy is absorbed by the wall. So if you want to talk in terms of destructive potential energies are best used.

However the thing that deforms the car, smashes the wall and kills people are the forces involved. The important thing is then the momentum and the time to stop. This is why crashes are sometimes described in terms of 'g forces' (acceleration)

As Cyosis pointed out a car moving at twice the speed only produces twice the force if it stops in the same time.

It further that point, say you are travelling at 200km/h in one car and 100km/h in the other. The 200km/h hits a large soft rubber wall and the 100km/h hits a brick wall. Although the faster car has 4x the energy at impact, but will suffer less damage as the forces are lower due to the impact event being much longer.

So to the OP: as you say identical cars hitting identical walls, the faster car will have more force at impact. This however is not because speed or KE but because the collision will give similar stopping times, and therefore a larger deceleration for the fater car.