A block of cheese hits a steel wall

[mrspeedybob]

...at greater then the speed of sound in cheese. The leading molecules of cheese cannot transmit the force of impact backward because the speed of force propagation is limited by the speed of sound in cheese so the molecules must move either sideways or into the steel. If the steel is strong enough then the only option is sideways. The area of impact may be large enough that the sideways velocity needs to be larger then the incoming velocity, but this would violate conservation of momentum. I can see the following possible solutions to this dilemma, but I don't know which, if any, are correct.

1. As the cheese hits the steel it compresses, forming a more dense medium through which force can be move rearward. I don't like this idea because it raises the problem of which moves rearward through the cheese first, force or compression. Compressing the cheese requires force, but the force cannot move backward because the cheese is moving forward faster.
2. I cannot treat the steel wall as rigid. It will deform to make room for the compressed cheese and/or cheese molecules will be forced in between metal atoms creating a cheese/steel mixture at the interface. I don't like this idea because replacing the steel with a stronger substance or replacing the cheese with a softer substance returns me to the original problem. Surely there is some combination of substances in which the wall can be treated as rigid and impermeable
3. There are conditions in which the propagation of force through a medium can be faster then the propagation of sound through the same medium. I don't like this idea because the transmission of sound is the transmission of force, it seems self contradictory.

So. Is there any truth to any of these? What is really going on at the cheese/steel interface?

 

[AlephZero]

If the steel is strong enough then the only option is sideways. The area of impact may be large enough that the sideways velocity needs to be larger then the incoming velocity, but this would violate conservation of momentum.

Momentum is a vector, not a scalar. The resultant momentum from all the "sideways" motion, in different directions, will be zero, however large the sideways velocities might be. So conservation of momentum is not violated by sideways motion of the cheese.

On the other hand, you didn't ask what happened to the momentum of the cheese perpendicular to the wall, which might seem to be reduced to zero. That is not the case because the momentum is actually transferred from the cheese to the earth, but the very large mass of the Earth means its change in velocity is too small to notice.

 

[cjl]

Note that the transmission of sound is the speed of the transmission of a compression wave in the limit of very low amplitude. A high amplitude compression wave will travel more quickly than the speed of sound (also known as a shock wave). So, a shock wave can propagate backwards through the cheese. In addition, the cheese will likely compress rather significantly at the cheese-wall interface,so it won't just flow directly outward at higher than the incoming velocity (which would violate conservation of energy, though it would actually not violate conservation of momentum).

 

[sophiecentaur]

(which would violate conservation of energy, though it would actually not violate conservation of momentum).

No violation if only a part of the cheese ends up going faster than the incoming lump. And this is what we observe in many collisions: parts fly off very much faster than the original objects. And that is in spite of the fact that most real-life collisions are not actually elastic.

 

[SteamKing]

Quick question. What is the speed of sound in cheese? Does it matter if the cheese is Camembert or Roquefort?

 

[sophiecentaur]

I imagine the speed wouldn't be very different except for the really hard cheeses. Cheese would almost certainly have very high sound absorbency. Good for recording studio walls, no doubt and handy for a spot of lunch too.

 

[Drakkith]

I imagine the speed wouldn't be very different except for the really hard cheeses. Cheese would almost certainly have very high sound absorbency. Good for recording studio walls, no doubt and handy for a spot of lunch too.

Silence your neighbors AND have a handy snack!

 

[JeffKoch]

Of course unless the studio is very chilly, the walls would gradually melt and rot, particularly in the summer. I think I would rather annoy my neighbors than attempt to record music in either a refridgerator or a room surrounded by purifying cheese.

But, of course the cheese compresses. Portions of the cheese block that are behind the impact front do not know they should slow down, stop, or move sideways, and so they pile up into the cheese in front that has been notified that it needs to change speed and direction. The cheese continues to move forward unimpeded until it crosses the back-propagating compression wave (a shock in the high-amplitude limit).

 

[Drakkith]

This thread deserves to be memorialized for all to experience the "cheesiness".

 

[cjl]

No violation if only a part of the cheese ends up going faster than the incoming lump. And this is what we observe in many collisions: parts fly off very much faster than the original objects. And that is in spite of the fact that most real-life collisions are not actually elastic.

Very true. It's fairly likely that a small portion of the incoming cheese will fly off much faster than the initial velocity, but it must be a relatively small portion such that the overall kinetic energy of the debris is less than the initial kinetic energy of the block of cheese.

 

[jetwaterluffy]

I was thinking of this myself, recently, although with a metal bar rather than cheese. Very interesting...