About man falling into grate paradox

[Nugatory]

Well I had a problem with the energy of the supposed stress, where does it come from, particularly in the still standing observers frame.

In all frames, there will be some period of time when the rod is sticking out over the edge, so that one end is supported by the ground underneath and the other end is not. This is just an ordinary cantilever, no different in principle from a balcony on the side of a building. The rod doesn't even have to moving relative to the hole for there to be stress in the rod: gravity is pulling the projecting end of the rod down into the hole, and is being resisted by stress forces within the rod.

 

[PAllen]

Well I had a problem with the energy of the supposed stress, where does it come from, particularly in the still standing observers frame.

I don't know what you mean by the still standing observer's frame.

The energy for the stress comes from work done on the rod - a great force (10^15 Newtons) does work on it, moving it distance (1 millimiter). The energy (work) applied to the rod, stressing it, is on the order of a terajoule (about 1% of the energy released by the Nagasiki atomic bomb). In rod frame (the only relevant frame for analyzing stress), this forice is not applied simultaneously, but from right to left (assuming the rod is moving left to right).

Following earlier suggestions, I proposed a piston pushing the rod down the hole. This has many advantages over gravity. Dealing with gravity (from a source that would have to specified) on an object moving near c relative to it, with gravity needing to be extremely strong field, would be a complex problem in GR. Also, the piston ensures that the rod is seen to remain horizontal in the grate frame.

But maybe that problem can be solved.

Let's see ... two rapidly spinning discs are pushed so that they slam together and fuse together, the result is a slowly spinning object. The spinning energy of the two disc system turned into stress energy of the discs, which stress energy turned into heat when the discs collided.

Is the above correct?

The discs are identical, they have identical angular momentum, and they collide with the flat parts first. And all velocities are relativistic.

The above is correct, but not very relevant the rod pushed through a grate hole.

 

[jartsa]

In all frames, there will be some period of time when the rod is sticking out over the edge, so that one end is supported by the ground underneath and the other end is not. This is just an ordinary cantilever, no different in principle from a balcony on the side of a building. The rod doesn't even have to moving relative to the hole for there to be stress in the rod: gravity is pulling the projecting end of the rod down into the hole, and is being resisted by stress forces within the rod.

No the ground never pushes the rod. In the man falling into grate paradox "It is assumed that the rod is entirely over the grate in the grate frame of reference before the downward acceleration begins simultaneously and equally applied to each point in the rod"

Quoted part is from the wikipedia.

 

[PAllen]

No the ground never pushes the rod. In the man falling into grate paradox "It is assumed that the rod is entirely over the grate in the grate frame of reference before the downward acceleration begins simultaneously and equally applied to each point in the rod"

Quoted part is from the wikipedia.

Of course, the key point being simultaneously in the grate frame = not simultaneously in the rod frame. Thus, for a given element of the rod, the element to its right (for example) accelerates down and to the left before any force or acceleration is applied to the given element.

 

[Nugatory]

No the ground never pushes the rod. In the man falling into grate paradox "It is assumed that the rod is entirely over the grate in the grate frame of reference before the downward acceleration begins simultaneously and equally applied to each point in the rod"

Quoted part is from the wikipedia.

Ah - right - yes, as I've seen the paradox described in other sources that part isn't always specified.

It's still something of a red herring though, because if you choose to use the grate frame you're just choosing to use a frame in which the problem is harder to analyze, hence leading to the apparent paradox. If you're going to insist on starting with the grate frame, you might try drawing the world lines of three points (each end and the middle of the rod) in such a way that the acceleration will be simultaneous in the grate frame. You'll see that these are also the world lines of those three points if the rod is being bent by the progressive application of force from one end to the other it its rest frame.