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

• castlegates
In summary, the conversation discusses the calculation of pounds per square inch exerted on a large block of steel when a one pound cube traveling at 600 MPH slams into it. The solution depends on the stiffness of the material, the acceleration of the cube, and the time it takes for the cube to stop. However, a rough estimate suggests a pressure of around 5 million PSI, but it is a complex problem that cannot be solved with simple physics.
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?

## The Attempt at a Solution

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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.

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.

mgb_phys said:
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?

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.

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.

mgb_phys said:
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?

Dick said:
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.

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?

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!

## 1. How is the pressure in pounds per square inch (psi) calculated?

The pressure in psi is calculated by dividing the force exerted on the large block of steel by the area of the block in square inches. This is represented by the formula P = F/A, where P is the pressure in psi, F is the force in pounds, and A is the area in square inches.

## 2. What is considered a high pressure in pounds per square inch?

The definition of high pressure can vary depending on the context, but in general, a pressure of 100 psi or higher is considered high. However, in some applications such as hydraulic systems, pressures can reach thousands of psi.

## 3. How does temperature affect the pressure in pounds per square inch?

As temperature increases, the pressure in psi also increases. This is because the molecules in the material or substance are moving faster and exerting more force, resulting in a higher pressure. The relationship between temperature and pressure is described by the ideal gas law: P ∝ T, where P is pressure and T is temperature.

## 4. Can the pressure in pounds per square inch be converted to other units of pressure?

Yes, the pressure in psi can be converted to other units such as bars, atmospheres, or pascals. The conversion factor will depend on the specific unit being converted to. For example, 1 psi is equal to 0.0689476 bars, 0.068046 atmospheres, and 6,894.76 pascals.

## 5. How can the pressure in pounds per square inch be measured accurately?

The pressure in psi can be measured using a pressure gauge or sensor. The accuracy of the measurement will depend on the precision and calibration of the instrument. It is important to regularly calibrate and maintain the instrument to ensure accurate readings.

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