Relativity, space contraction and rotation

In summary, a bar with length l = 10mm is moving along the x-axis with speed v in referential R. A table with a circular hole of radius r = 5mm is moving along the z-axis with speed u, parallel to the bar. From R's perspective, the bar fits the hole, but from R', at rest in relation to the bar, the hole appears smaller. It is asked if it makes sense to ask how the bar fits in the hole. The problem also asks to show that in R', the bar and table are no longer parallel, with an angle A between them and tg(A) = uvg/c², g= sqrt(1/(1-v²/c²)). Furthermore, it
  • #1
imphat
10
0

Homework Statement


A bar (lo = 10mm) is moving along the x-axis with speed v according to a referential R.

Meanwhile a table, parallel to the bar is moving along the z axis, with speed u. There's a circular hole in the table with radius = 5mm.

From R perspective the bar has l < 10mm and it fits the hole on the table. But, from the point of view of R', resting in relation to the bar, the hole is smaller than the length of the bar.

A. Does it make sense to ask how the bar fits in the hole? Explain

B. show that in R' the bar and the table are no longer paralel, and there's a angle A between them and tg(A) = uvg/c², g= sqrt(1/(1-v²/c²))

C. show that the point C, in the middle of the whole approaches the point B, in the middle of the bar following the line z'=-u/gv x'

Homework Equations


The Attempt at a Solution


Im really clueless here. Anyone care to explain this problem to me?
 
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  • #2
Hi imphat! :smile:

Hint: leave A until you've done B and C.

Can you do B? What have you tried? :smile:
 
  • #3
hi tim, thanks for the fast reponse once again

the only thing i did so far was to draw some drafts of what happens...

i was thinking maybe rotating the axis on the R' referential, in a way that the movement of the hole is done along 1 single direction, let's say, the z' axis... but i really don't see how the table gets not to be parelel to the bar on R'
 
  • #4
… avoid doom …

Hi imphat! :smile:

No no no …

In relativity, trying to think up a logical answer usually spells doom.

You have to apply the Lorentz equations!

Just to start you off …

Two corners of the table are at (t,a,0,ut) and (t,b,0,ut) in R (with a and b constant).

So where are they in R´? :smile:
 
Last edited:

1. What is the theory of relativity?

The theory of relativity is a scientific theory developed by Albert Einstein in the early 20th century that describes how objects behave in the presence of gravity. It is divided into two parts: the special theory of relativity, which deals with objects moving at constant speeds, and the general theory of relativity, which deals with objects in accelerated motion.

2. How does relativity affect space and time?

According to the theory of relativity, space and time are not absolute concepts. They are relative and can change based on the observer's perspective and the speed of the objects in question. This means that time can appear to move slower or faster depending on the speed of an object, and objects can appear to contract or expand in size based on their velocity.

3. What is space contraction?

Space contraction, also known as length contraction, is a phenomenon predicted by the theory of relativity. It states that objects in motion will appear shorter in the direction of their motion when observed by someone at rest. This is because the faster an object moves, the more it will experience time dilation and the less distance it will cover in a given amount of time.

4. How does rotation affect relativity?

Rotation can affect relativity in several ways. First, it can cause time dilation, where time appears to pass slower for objects in motion compared to those at rest. Second, it can cause space contraction, as objects rotating at high speeds will appear to be shorter in the direction of their rotation. Finally, rotation can also cause gravitational effects, as spinning objects can create gravitational fields that can warp space and time.

5. How has the theory of relativity been proven?

The theory of relativity has been proven through numerous experiments and observations. Some of the key evidence includes the observations of the bending of starlight near massive objects, the confirmation of time dilation through atomic clocks, and the precise predictions of the orbits of planets in the solar system. Additionally, the theory has been mathematically verified and is widely accepted by the scientific community.

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