# Solid - solid impact force peak

1. Nov 17, 2013

### pixelpuffin

how would i go about calculating the peak force of an impact between two solids
i assume it has to do with the how readily the structure compresses but im not sure what else might complicate it from there
also what if one of the objects fractures and what about granular impacts

2. Nov 18, 2013

### CWatters

It's very hard unless you make assumptions.. Consider dropping a ball onto something soft like clay...

If the ball comes to a stop making an impression "s" meters deep then you can estimate the peak deceleration "a" using the equations of motion....

V2 = U2 + 2as

where

V=0
U = Impact velocity

Solve for "a"

Then use F = ma to calculate the force.

However this assumes the impact is non-elastic and constant deceleration.

If the situation is more complicated (eg the second object fractures) you could use another method (such as high speed camera) to measure the deceleration of the first object directly.

3. Nov 18, 2013

### ZapperZ

Staff Emeritus

For example, bring two solids slowly together until they finally touch. Now, compare this to slamming those two very, very hard. Do you think there's a difference in "peak force of an impact between two solids"?

You emphasized on the nature of the solid itself when you ignore information on the most important aspect of an impact, the velocity of the collision itself! I've tried to illustrate to you something obvious that you should already be aware of that is a big part of trying to analyze such a situation.

Zz.

4. Nov 18, 2013

### pixelpuffin

i need an equation for extremely high speed (3000 meters per second maybe) most of the time involving metals and ceramics
although a high estimate will work to as long as its always a high estimate

5. Nov 19, 2013

### CWatters

I suspect you won't find it on a general physics forum although someone might surprise us. At those sort of speeds the energy will be enormous. More like an explosion than impact. Might be meaningless to talk about a "peak force" when everything is turned into a gas?

6. Nov 19, 2013

### pixelpuffin

id like to see just how large of a projectile is needed to survive and various angles

7. Nov 19, 2013

### AlephZero

Your impact speed is the same order of magnitude as the speed of sound in most engineering materials, so you are out of the range of any "simple" approximations to what happens.

Almost by definition, the stress can't exceed the crushing stress of the material, without breaking something. If you don't want to do any modeling of the impact, that is probably as good a "maximum force" estimate as anything else.

But material properties depend on the strain rate, so you won't find good quality good material data for high velocity impacts just lying around on the web.