A pole, 2 lightyears in length - conceptual question

[DaveC426913]

If you suddenly move one end, you'll create a shockwave that propagates faster than the speed of sound.

You haven't been following along. You'll create a shockwave that will travel at the speed of sound of the material of which the object is made.

Wow! This post makes me laugh. This seems like a simple conceptual question from a basic modern physics course, but it has been severely over-analyzed in this post.

Your right. The other end does not move, because it would violate one of the postulates of special relativity; nothing travels faster than light speed. Problem solved.

Obviously you memorized your equations in school and never bothered to understand them. Because if you placed any value in understanding, you would never have posted that.

It is easy to say something violates a law. That doesn't help the OP understand where he's thinking about it wrong. Or lead him to the correct answer.

Which is what we like to do here.

 

[buffordboy23]

Obviously you memorized your equations in school and never bothered to understand them. Because if you placed any value in understanding, you would never have posted that.

It is easy to say something violates a law. That doesn't help the OP understand where he's thinking about it wrong. Or lead him to the correct answer.

Which is what we like to do here.

Whatever. The solution to the problem does not ask us to think this way b/c it does not give us enough info.

On top of that, the OP never stated any assumptions (of this own choosing or from the text) concerning the properties of the pole. If he assumes (or the text) that it is an ideal rigid body (i.e., the distance between mass elements of the pole is constant, always - which is usually the case in introductory texts), then we have just violated special relativity. However, on the contrary, we must acknowledge the fact that no body is truly an ideal rigid body, and thus the most realistic answer is the one in which you have just prescribed.

This is the answer, but where is the subsequent post from the author of the OP that shares his (or her) thoughts concerning this discussion? Absent. Great work.

 

[DaveC426913]

Whatever. The solution to the problem does not ask us to think this way b/c it does not give us enough info.

We don't wait to be told how to think. In a discussion that can span days instead of seconds, it makes sense to anticipate the next question.

And the question does give us enough info. We know why the end of the pole doesn't instantly move. It's because we know the pole is not rigid. If the OP had been assuming a non-existently rigid pole he would have had to state that.

 

[buffordboy23]

A pole in zero gravity, two light years in length

you push it 1m,

does it move instantly at the other end?

There are two answers. Yes, if the pole is an ideal rigid body, which shows that ideal rigid bodies are not compatible with special relativity. No, if the pole is not an ideal rigid body, because the force must transmitted from atom to atom through the pole, which is slower than the speed of light.

The author of the text phrased the problem so that you would recall one of the postulates of special relativity. The "two light-years in length" flips the switch for the student. It's really an awkward question and could be improved by generalization; i.e., the pole can be of any length (say, 1 meter) and when you push the one side causing an incremental displacement dx of that side, does the other side move instantaneously with a displacement of dx. Think about that the next time you are pushing furniture around the house.

 

[Mentallic]

Think about that the next time you are pushing furniture around the house.

Well no wonder it takes so long to do so!

 

[DaveC426913]

There are two answers. Yes, if the pole is an ideal rigid body

Why would we assume something that does not exist? With that logic, we might as well assume invisible elves too.

 

[Count Iblis]

You'll create a shockwave that will travel at the speed of sound of the material of which the object is made.

Don't shock waves always travel faster than the local velocity of sound? We are not talking about an infinitessimal perturbation of the local density here. We are moving one end of the pole by a finite amount. I would like to see a detail analysis from first principles of this problem. Let's take a cylindrical pole of length L, cross section A with elasticity modulus E, Poisson ratio nu, and density rho.

Then we're going to move one end by a finite amount of d ising some impulse force. So, we have to think about the appropriate initial conditions. We can't just take the stress tensor at the boundary to have some intial value, we must make sure that there is some actual finite displacement in a finite time in the limit that L goes to ininity.

 

[buffordboy23]

Why would we assume something that does not exist? With that logic, we might as well assume invisible elves too.

Does someone have a grudge?

How about this reason? B/c a large number of the ideas in introductory physics assume such idealized notions, and it becomes part of the student's thinking when solving problems. When the student gets to more advanced classes, these ideals are shown to be adequate. It's illustrative to see why an assumed ideal model can be successful in some domains, but not in others.

 

[DaveC426913]

Don't shock waves always travel faster than the local velocity of sound?

Not sure, but it does seem that the speed of the shock wave must at least start at the speed of the impacting force, which easily can be faster than the speed of sound in the material. I think the shockwave degenerates to a normal sound wave over time.

 

[turin]

I think the question of what would "really" happen, in terms of sound propagation, is just too complicated. Notice that the OP does not specify how quickly the near end moves. It could take years to move 1 meter. I think that, if it is moved slowly enough, then the elastic response can be treated linearly. If the near end of the rod is pushed as fast as possible (let's say much faster than the speed of sound in the material of the rod), then I would assume majorly nonlinear phenomena (i.e. shockwave), at least initially, and I wouldn't know how to sort that out. The speed of sound can depend on frequency and amplitude.

 

[DaveC426913]

I think the question of what would "really" happen, in terms of sound propagation, is just too complicated.

No, it just means you lay out the multiple cases and state your assumptions in each, as you just did.

 

[DaveC426913]

Does someone have a grudge?

As someone who entered the thread with "This thread makes me laugh. ... it has been severely over-analyzed..." I think you have no complaint if you don't like the response you get.

How about this reason? B/c a large number of the ideas in introductory physics assume such idealized notions, and it becomes part of the student's thinking when solving problems. When the student gets to more advanced classes, these ideals are shown to be adequate. It's illustrative to see why an assumed ideal model can be successful in some domains, but not in others.

I agree, considering an idealized case is a perfectly valid technique, but in this case, the answer is right in front of him; it is unnecessary to idealize (i.e. modify) the scenario. The basic question has a basic answer; the "real" physics case is more valid than the "idealized" case.

 

[buffordboy23]

As someone who entered the thread with "This thread makes me laugh. ... it has been severely over-analyzed..."

It wasn't my best post, but its character remains true. Obviously, the student is looking for a simple explanation, but the thinking goes way beyond and requires assumptions (besides the ideal rigid body case) that are not given. You and other PFers even said so in previous posts.

I think you have no complaint if you don't like the response you get.

You can criticize the content of my response all you want. This is just one process of how science works. However, when you criticize the individual (me), this is when we will have problems.

I agree, considering an idealized case is a perfectly valid technique, but in this case, the answer is right in front of him; it is unnecessary to idealize (i.e. modify) the scenario. The basic question has a basic answer; the "real" physics case is more valid than the "idealized" case.

Yes, but this is not his thinking in the OP and his subsequent posts. He accepts the notion that nothing can travel faster than the speed of light, yet the solution to the problem does not make sense to him. He doesn't explicitly state the assumptions regarding the problem, but he does assume that the pole is an ideal rigid body. This is evident b/c his inexperience leads him to the equations of special relativity, which is the wrong approach here. These two ideas (speed of light and ideal rigid body) are in conflict, and rightly so. He must abandon the idea that the pole is an ideal rigid body to understand the realistic answer here.

 

[DaveC426913]

You can criticize the content of my response all you want. This is just one process of how science works. However, when you criticize the individual (me), this is when we will have problems.

I was criticizing the individual, yes. Laughing in derision is not a valid argument, it is an attack.

Anyway, water under the bridge. You've recovered from it.

Yes, but this is not his thinking in the OP and his subsequent posts. He accepts the notion that nothing can travel faster than the speed of light, yet the solution to the problem does not make sense to him. He doesn't explicitly state the assumptions regarding the problem, but he does assume that the pole is an ideal rigid body. This is evident b/c his inexperience leads him to the equations of special relativity, which is the wrong approach here. These two ideas (speed of light and ideal rigid body) are in conflict, and rightly so.

He must abandon the idea that the pole is an ideal rigid body to understand the realistic answer here.

Yes, which is why your simple answer that it violates relativity doesn't help him much. It is only incidentally a relativity issue. The most important issue is to recognize that the rod is not rigid. This principle would apply even if relativity were not a factor.

For example, if the OP went away thinking this was a relativity issue, he might logically conclude that a normal rod (say, made of wood) of extraordinary length could move both ends almost simultaneously, as long as the transmission was less than c. He would not be much better off; he would still be missing the point by many, many orders of magnitude.

 

[Count Iblis]

At high school level it happens quite often that teacher will give a simple but misleading or even flawed explanation to students.

 

[buffordboy23]

Yes, which is why your simple answer that it violates relativity doesn't help him much.

I disagree. It answers his question by illustrating that his belief that the pole is an ideal rigid body is a misconception.

It is only incidentally a relativity issue. The most important issue is to recognize that the rod is not rigid. This principle would apply even if relativity were not a factor.

Like I said before, it's a really awkward question. The question would be just as valid if we were talking about a 1 meter^3 block (although the results would vary dramatically); the original problem was designed to make the answer stand out. The only aspect from relativity that comes into play is that no transmission is greater than c.

For example, if the OP went away thinking this was a relativity issue, he might logically conclude that a normal rod (say, made of wood) of extraordinary length could move both ends almost simultaneously, as long as the transmission was less than c. He would not be much better off; he would still be missing the point by many, many orders of magnitude.

Yes, I agree. This is great for further understanding but it was not his question. Others already touched on it, so I chose to focus only on the misconception. It is good to discuss though, but it looks like the OP has left the building (this thread) a while ago.

 

[buffordboy23]

At high school level it happens quite often that teacher will give a simple but misleading or even flawed explanation to students.

I agree. I would also suggest that it often happens where the teacher gives explanations way over the student's head.