How many pounds per square inch is exerted on the large block of steel

[castlegates]

Homework Statement

Don't know how to calculate this. Not sure I care either, but I figured you people do care and know. I'm having a little dispute with someone about pounds per square inch of say an object moving at a high rate of speed on impact with say steel. So here is the scenerio. Let's take a square inch cube that weighs in at one pound, and is traveling at 600 MPH, and it slams one of it's square faces into a large block of steel. The question is how many pounds per square inch is exerted on the large block of steel?

Homework Equations

The Attempt at a Solution

 

[mgb_phys]

It depends on how quickly it stops.
PSI is a measure of force/area (pounds in this case are force not mass !)
Force is mass * acceleration.
To know the force you have to know the accelaration, that is how quickly the small block comes to a stop in the large block.
This depends on the stiffness of the material and lots of tricky details about how it deforms. You normally measure this experimentally or simulate it on a computer using Computaton Fluid Dynamics / Finite element analysis.

 

[Dick]

You could always do a guesstimate. A reasonable estimate is that the collision time is about the time it takes a sound wave in steel to travel an inch. I was going to guess that it does more of a bounce than a cold stop. 600MPH isn't THAT fast. As mgb_phys says, a real answer would cost you. An estimate probably wouldn't be off by a factor of more than ten. The price for that is just saying that you care enough to try to do it yourself and want some help. It's not that hard.

 

[castlegates]

It depends on how quickly it stops.
PSI is a measure of force/area (pounds in this case are force not mass !)
Force is mass * acceleration.
To know the force you have to know the accelaration, that is how quickly the small block comes to a stop in the large block.
This depends on the stiffness of the material and lots of tricky details about how it deforms. You normally measure this experimentally or simulate it on a computer using Computaton Fluid Dynamics / Finite element analysis.

Lets just say the cube comes to a dead stop when it hits, that means the entire mass of the cube comes to a dead stop. How many pounds per square inch is exerted? Rough estimate?

 

[mgb_phys]

Thats the point what is a 'dead stop',
Ignoring how the cube deforms, and just using f=ma
If it takes 1 millisec to stop = 27,000 psi, if it takes 1 microsec = 27,000,000 psi, if it stops instantly there is an infinite pressure.

As dick said, the minimum time for anything to happen is around the speed of sound, say 4500m/s for steel. So traveling 1inch it takes 1/180,000 s, or 5us, giving a pressure of around 5Million PSI.

 

[Dick]

Momentum is m*v=p. Force is change in p over change in time. We need to estimate the stopping time (t=0 would mean infinite force). Like I said, let's try the time it takes sound in steel to travel 1 inch. That's 1*inch/(1500*m/sec)=4*10^(-5)*sec. Mass of a cubic inch of steel is about 0.1kg. 600*mi/hr is about 300*m/sec. So p=30*kg*m/sec. p/t=10^6*N. (N=Newton=kg*m/sec^2). 1 lb force is about 4N. So I would call it about 200000 psi. Plus or minus a LOT.

 

[Dick]

Thats the point what is a 'dead stop',
Ignoring how the cube deforms, and just using f=ma
If it takes 1 millisec to stop = 27,000 psi, if it takes 1 microsec = 27,000,000 psi, if it stops instantly there is an infinite pressure.

As dick said, the minimum time for anything to happen is around the speed of sound, say 4500m/s for steel. So traveling 1inch it takes 1/180,000 s, or 5us, giving a pressure of around 5Million PSI.

Ooops. Just realized I was using the speed of sound in water. Triple my estimate. What else did I underestimate?

 

[mgb_phys]

Ooops. Just realized I was using the speed of sound in water. Triple my estimate. What else did I underestimate?

And I realized I used the OP's 1lb for the mass of the block without checking - sorry I'm used to metric don't have a feel for what a cubic inch of metal weighs.

 

[castlegates]

Sorry guys. this is obviously much more complicated than I thought, and requires some very specific parameters to arrive at anything close to a real estimate, but we can at least say thousands of PSI if the cube is made of aluminum up against steel?

 

[mgb_phys]

Yes - it is unfortunately one of those questions that you can't do with simple physics.
But you can say that there wouldn't be much left of the aluminium block!