Impact of a cannonball on a brick wall

[nave10]

If you had a cannonball made that was 5 pounds in weight and it hit a brick wall at a speed of 1,000 miles per second at the point of impact, how many pounds of pressure per square inch would the cannonball exert on the brick wall?

 

[TGlad]

Doesn't sound like a serious question Nave, but, giving you the benefit of the doubt:

Firstly, pressure is force per area, so you can't answer the question without knowing properties of the brick, and the value would change over time. Finding an impulse per area would be easier.
Secondly, a cannonball doesn't have a clear cross sectional area, and even if it did, you haven't specified the size of the cannonball.
Thirdly, you have yourself a very fast cannonball.

 

[nave10]

The cannonball is 5 inches in diameter and made of lead.

 

[DaveC426913]

The cannonball is 5 inches in diameter and made of lead.

At those kinds of speeds, it'll matter where you measure that diameter - transverse to the line of motion - or aligned with it.

 

[Lsos]

I'm not sure you can answer this question without using a supercomputer or an experiment. There's too many variables.

A supercomputer probably, as an experiment of this magnitude is impossible for our below Type I civilization.

 

[willem2]

I'm not sure you can answer this question without using a supercomputer or an experiment. There's too many variables.

A supercomputer probably, as an experiment of this magnitude is impossible for our below Type I civilization.

Well, at these speeds, some things make it simpler. Since the kinetic energy is so much bigger than the intramolecular forces and chemical bonds of the ball and the brick wall, the only thing that matters will be the mass of the ball, and of the section of wall in front of it.

A 5-inch ball of lead weighs 12 kg. The speed is 1.6 * 10^6 meters/second, so the
kinetic energy of the ball is 1.5 * 10^13 J. This is equal to about 4 kiloton of tnt, or about 1/4 times the Hiroshima bomb. If the section of the wall in front of the ball would also weigh 12 kg, you'd have half of the kinetic energy available for an explosion. If the wall was thinner, you'd get less energy, but I'm sure there would be nothing left of the cannon ball or the brick wall anyway.

You'd better fire the ball in vacuum, because the heat produced by air friction, would produce a shock wave and radiation, and the ball wouldn't get very far before evaporating or exploding. (the ball will meet about a 1 kg of air in the first 100 meters), so about
10^12 J of heat energy would be produced.

 

[jetwaterluffy]

It will depend if the wall fully stops the cannonball, how fast it spots it, and how much of the cannonball touches the wall at anyone time.

 

[nave10]

Getting back to my original question. When I think of force, the only thing I am concerned with is the approximate pounds of pressure per square inch. I have tried several physics calculators online and when I plug in the variables such as the weight of the ball and the speed at which it's travelling, I get figures that do not explain how much force the 5 pound metal ball, 5 inches in diameter hits a brick wall. I'm not concerned about what happens to either the ball or the wall. I merely want to know how much force per square inch that projectile is going to hit a solid object traveling at 1,000 feet per second, which is a slower speed than most bullets.

 

[DaveC426913]

that projectile is going to hit a solid object traveling at 1,000 feet per second, which is a slower speed than most bullets.

Ah.

Your opening post says

... a speed of 1,000 miles per second ...

(Yeahyeah, go check. We'll wait.)


1,000 miles/s is a sizeable fraction of the speed light. Which is why everyone is looking at you askance, and why you are getting answers that, to you, probably make little sense.

 

[Danger]

1,000 miles/s is a sizeable fraction of the speed light. Which is why everyone is looking at you askance, and why you are getting answers that, to you, probably make little sense.

I was trying to think up a way to mention that without sounding condescending. All that I could think of is, "Get the hell away from there before the gamma flash from the impact comes back at you."

 

[TGlad]

Lets use SI units, and pretend that the ball is a cylinder since you can't get a single cross section area from a sphere impact:

5 inches diameter is about 0.0625m radius which is about 0.0123m^2 cross sectional area
1000 feet per second is 3280 metres per second.
5 pounds is 2.26 kg
So if the brick wall completely stopped the cannonball then there would be an impulse per area of 3280*2.26/0.0123 ≈ 600,000 kg m/s per square metre.

If the brick wall only halved the cannonball's speed then you'd get half this value. How much the cannonball slows down from the impact depends on the weight and strength of the wall.

To get an average pressure you'd have to divide the result by the time period over which the cannonball is in contact with the wall.