exploding bowling ball

[rthmjohn]

Sorry if this thread doesn't belong here, but I didn't know exactly which branch of physics it belonged to.

 

So anyway, I was taking a placement test for a science club at school and one of the questions went something like this:

 

"A pilot of an aircraft is flying over the ocean, when all of a sudden, he accidentally releases his explosive bowling ball. To avoid wasting a good bomb, he detonates the accelerating ball in mid-air and it bursts into exactly 1000 identical pieces of 10g each. Surprisingly, the blast generates neither sound or heat. Explain what happened."

 

Anybody have any Ideas?

[studytogethe]

the bowling ball can be explode ??????

 

____________________

http://studytogether.x.am

[YT2095]

my GUESS, is that "Bowling Ball" is a code or nickname for a cluster bomb, making what`s known as "Steel Rain", they consist of many tightly packed Bomblets that seperate in mid air above a target area (no heat and little sound at this point) they cover a wide area and the bomblets explode on impact.

[Phi for All]

Could the "aircraft" be a shuttle in orbit? That would account for no heat or sound. The "bowling ball" (very heavy at 10kg/22 pounds) could have exploded due to the vacuum of space (except it states that the pilot exploded it manually).

 

To me, calling the bomb an exploding bowling ball implies it's shape is round. It also must have had an explosive to propel the pieces and some kind of radio device. Perhaps this is reading too much into it, but the fact that the pieces are identical seems more surprising than the fact that there was no heat or sound (unless it was manufactured that way, as YT2095 suggests).

[YT2095]

actualy if it wasn`t for the Identical peices, I`de have though the rapid cooling of the oustide causing shrinkage as happens at altitude would have been the pressure required to make it explode if a round was fired at it, creating a weakness and then rupture, I say a round as that wouldn`t be the bowling ball making the sound then and it would be more or less heat free AND the pilot would have an active roll in deciding When it blew

 

it`s the identical pieces that got me thinking, and that it was 10g each (ideal for a cluster bomb AKA "Steel Rain").

 

though it`ll prolly be something really simple, and we`ll all be complaining "Why wasn`t this posted in the Brainteasers forum!" )

[J.C.MacSwell]

actualy if it wasn`t for the Identical peices' date=' I`de have though the rapid cooling of the oustide causing shrinkage as happens at altitude would have been the pressure required to make it explode if a round was fired at it, creating a weakness and then rupture, I say a round as that wouldn`t be the bowling ball making the sound then and it would be more or less heat free AND the pilot would have an active roll in deciding When it blew

 

it`s the identical pieces that got me thinking, and that it was 10g each (ideal for a cluster bomb AKA "Steel Rain").

 

though it`ll prolly be something really simple, and we`ll all be complaining "[b']Why wasn`t this posted in the Brainteasers forum[/b]!" )

 

That's what I was thinking. Some trick, like an endothermic explosion with noone around to hear it, so it isn't "sound", merely compression waves in air like the tree in the forest thing. The pilot flys off at greater than mach 1 so he doesn't get to hear it.

 

But that's probably not it.

[Phi for All]

The pilot flys off at greater than mach 1 so he doesn't get to hear it.

But this doesn't mean sound isn't generated, and that is stated specifically.

 

"He detonates the accelerating ball in mid-air..." Is this a red herring or is it a key to the solution? Also, why an exploding bowling ball instead of just a bomb? And if he doesn't want to waste it why set it off? Does flying over the ocean have any significance or is it just so the bomblets won't hurt anyone?

[swansont]

But this doesn't mean sound isn't generated' date=' and that is stated specifically.

 

"He detonates the [b']accelerating[/b] ball in mid-air..." Is this a red herring or is it a key to the solution? Also, why an exploding bowling ball instead of just a bomb? And if he doesn't want to waste it why set it off? Does flying over the ocean have any significance or is it just so the bomblets won't hurt anyone?

 

Oh, for crying out loud, it's a physics problem! (this is not directed just at you, Phi)

 

The acceleration is because it's falling under the influence of gravity. The lack of sound and heat means you can treat it as an elastic collision - KE is a conserved quantity at the point of explosion, and because the energy conversion is internal, momentum is also conserved at the time of the explosion.

 

The center of mass of the fragments will have a certain behavior that one can describe, subject to those conditions. That's what needs to be answered.

[J.C.MacSwell]

Oh' date=' for crying out loud, it's a physics problem! (this is not directed just at you, Phi)

 

The acceleration is because it's falling under the influence of gravity. The lack of sound and heat means you can treat it as an elastic collision - KE is a conserved quantity at the point of explosion, and because the energy conversion is internal, momentum is also conserved at the time of the explosion.

 

The center of mass of the fragments will have a certain behavior that one can describe, subject to those conditions. That's what needs to be answered.[/quote']

 

You can accomplish this with 1000 identical pieces of 10 grams each?

[swansont]

You can accomplish this with 1000 identical pieces of 10 grams each?

 

You aren't going to solve for the trajectory of each (as opposed to the standard problem of it splitting into two pieces), but there are statements that can be made about the behavior, with the given information. Specifically, the center-of-mass motion is unaffected because momentum is conserved, and you can predict the impact point of the COM. You expect a distribution of particles about that point.

[J.C.MacSwell]

You aren't going to solve for the trajectory of each (as opposed to the standard problem of it splitting into two pieces), but there are statements that can be made about the behavior, with the given information. Specifically, the center-of-mass motion is unaffected because momentum is conserved, and you can predict the impact point of the COM[/b']. You expect a distribution of particles about that point.

 

In a vacuum yes, but total drag goes way up. So the COM will not follow the trajectory it would have unexploded. (it will fall short)

 

But my point was more to do with what kind of explosion you envisioned. Some kind of flywheel equivalent that flies apart?

 

There seems to be more extraneous information than your run of the mill physics problem and yet not enough information to find a solution. That's why it looks more like a brain teaser.

[rthmjohn]

Just for the record, this question was PHYSICS related as it was under the physics portion of the test, and the bowling ball was an actual bomb... and the pilot was flying over an ocean, which is why he set it off in mid-air. Otherwise he would have had to scuba dive in the ocean to recover it

[rthmjohn]

Swansont, I think you might know the answer. I know very little about physics, but I think this problem has something to do with conservation of certain energies and what not. Do you think you could explain your reasoning to me so that I might understand. FYI, this problem REALLY bugged me, but maybe if I had taken physics as a sophomore, I wouldn't be so bad off.

[swansont]

Swansont, I think you might know the answer. I know very little about physics, but I think this problem has something to do with conservation of certain energies and what not. Do you think you could explain your reasoning to me so that I might understand. FYI, this problem REALLY bugged me, but maybe if I had taken physics as a sophomore, I wouldn't be so bad off.

 

As I implied before, in the absence of any forces in the x-direction, the momentum will be conserved, so the COM motion will be exactly the same as if the ball didn't explode. So if you know the horizontal speed and the height, you can find the COM impact point. The energy assumption means that it can be treated just like a completely inelastic collision at the moment of explosion (I mistakenly wrote elastic earlier) - all of the energy of the explosion converts to kinetic energy of the shrapnel. (If there were only two pieces, you could actually solve for the trajectories: two unknowns and two equations, from momentum and kinetic energy. This version is a standard first-semester physics problem.)

[J.C.MacSwell]

As I implied before, in the absence of any forces in the x-direction, the momentum will be conserved, so the COM motion will be exactly the same as if the ball didn't explode[/b']. So if you know the horizontal speed and the height, you can find the COM impact point. The energy assumption means that it can be treated just like a completely inelastic collision at the moment of explosion (I mistakenly wrote elastic earlier) - all of the energy of the explosion converts to kinetic energy of the shrapnel. (If there were only two pieces, you could actually solve for the trajectories: two unknowns and two equations, from momentum and kinetic energy. This version is a standard first-semester physics problem.)

 

The air resistance effects force components in both the x and y directions and would considerably affect the trajectory of the COM and point/s of impact.

 

I mentioned earlier it would fall short, but if the x component of velocity was small enough it could "fly" farther (than otherwise) due to the extended time in the air due to the y component drag being more signicant than the decceleration in the x direction.

 

But if it "exploded" while still accelerating after a typical drop from an airplane the COM of the fragments should fall considerably short assuming still air.

[swansont]

I think there's a reasonably good chance that "ignore air resistance" is part of the original question, as in most introductory physics course problems, and wasn't included in the paraphrased version.

[rthmjohn]

Thanks, swansont. I still don't completely understand what momentum or COM impact are, but I now know why the ball doesnt generate heat or sound.

 

To YT: Turns out this post actually belonged here!!! :)

[Jacques]

Surprisingly, the blast generates neither sound or heat.

 

I thaught that was the question: why no sound or heat.? I didn't see it as a question about the 1000 pieces trajectory...

[J.C.MacSwell]

As I implied before, in the absence of any forces in the x-direction, the momentum will be conserved, so the COM motion will be exactly the same as if the ball didn't explode. So if you know the horizontal speed and the height, you can find the COM impact point. The energy assumption means that it can be treated just like a completely inelastic collision at the moment of explosion (I mistakenly wrote elastic earlier[/b']) - all of the energy of the explosion converts to kinetic energy of the shrapnel. (If there were only two pieces, you could actually solve for the trajectories: two unknowns and two equations, from momentum and kinetic energy. This version is a standard first-semester physics problem.)

 

I'm still not sure where the collision (or equivalent) is but isn't heat generated in inelastic collisions, but not elastic ones?

[swansont]

I'm still not sure where the collision (or equivalent) is but isn't heat generated in inelastic collisions, but not elastic ones?

 

Yes, but of you run the explosion backwards it looks like a completely inelastic collision, with all the energy that would normally go into heat, sound and deformation being stored up as the explosive potential energy.

[swansont]

I thaught that was the question: why no sound or heat.? I didn't see it as a question about the 1000 pieces trajectory...

 

No, the "no sound and no heat" is a way of letting the solver make certain assumptions about the system. It's standard physics-question jargon, like "an elephant whose mass may be ignored..."

[J.C.MacSwell]

Yes, but of you run the explosion backwards it looks like a completely inelastic collision, with all the energy that would normally go into heat, sound and deformation being stored up as the explosive potential energy.

 

A reversed inelastic collision? Isn't there a law against that?

 

I guess if you used pressurized air at ambient temperature it would ideally lose heat during an explosion/expansion so theoretically it could be done in a way that no net heat is gained or lost and entropy is increased.

[swansont]

A reversed inelastic collision? Isn't there a law against that?

 

I guess if you used pressurized air at ambient temperature it would ideally lose heat during an explosion/expansion so theoretically it could be done in a way that no net heat is gained or lost and entropy is increased.

 

In reality, yes, it probably violates the second law of thermodynamics if it was a macroscopic object. If it was a nuclear system, you'd be fine (nowhere else for the energy to go). But solving idealized problems for introductory physics is the rule, rather than the exception - no friction, no air resistance, etc. But many problems are best solved in an idealized case, accounting for perturbations afterward, instead of trying to set up an exact solution from the beginning.

[J.C.MacSwell]

In reality, yes, it probably violates the second law of thermodynamics if it was a macroscopic object. If it was a nuclear system, you'd be fine (nowhere else for the energy to go). But solving idealized problems for introductory physics is the rule, rather than the exception - no friction, no air resistance, etc. But many problems are best solved in an idealized case, accounting for perturbations afterward, instead of trying to set up an exact solution from the beginning.

 

I guess that's the problem with the problem as stated. If you assume it is an introductory physics problem, strip away all the extraneous information, and take "surprisingly the elephant has no mass, please explain" to be code for ignore the elephant's mass then there is really nothing left to explain or solve. It is just a story about a flea walking away unharmed.

[swansont]

I guess that's the problem with the problem as stated. If you assume it is an introductory physics problem, strip away all the extraneous information, and take "surprisingly the elephant has no mass, please explain" to be code for ignore the elephant's mass then there is really nothing left to explain or solve. It is just a story about a flea walking away unharmed.

 

Part of the issue here is that the question was paraphrased, not stated, so I admit I am reading a little into it, but I taught physics for a number of years, so I'm drawing on my experience there.

 

The "elephant whose mass may be ignored" is an inside joke mocking some of the approximations we make, as is the "let's assume a spherical cow" joke:

 

A dairy farmer is in a fit of desperation over the fact that his cows won't give enough milk. He talks to farmers, biologists, etc. and they can't help him. Finally he consults a theoretical physicist about the problem. The physicist listens to him, asks a few questions, and then says he'll take the assignment. A few weeks later, he calls up the farmer, and says "I've got the answer." They arrange for him to give a presentation of his solution to the milk shortage.

 

When the day for the presentation arrives, he begins his talk by saying, "First, we assume a spherical cow..."

 

 

(and I've spoofed that joke here)