Length contraction problem of right angled triangle

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Discussion Overview

The discussion revolves around the implications of length contraction on a right-angled triangle when it is observed from a moving frame. Participants explore how the sides of the triangle may contract differently due to their orientation relative to the direction of motion, raising questions about the preservation of the triangle's shape and angles in the moving frame.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant describes a scenario where a right-angled triangle is moving at speed v perpendicular to its hypotenuse, questioning whether it remains a right triangle due to length contraction.
  • Another participant suggests that the hypotenuse, being perpendicular to the direction of motion, does not undergo length contraction, while the legs of the triangle contract differently based on their orientation.
  • A participant expresses confusion about why the lengths of the sides appear to tilt towards the hypotenuse and questions the mechanics behind this change in position or angle.
  • One participant uses an analogy of stacked rods to illustrate how each rod contracts according to the direction of motion, leading to a shape that outlines the triangle, despite the contraction.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the implications of length contraction for the triangle's shape. There are competing views on how the sides contract and whether the triangle retains its right-angle properties in the moving frame.

Contextual Notes

Participants express uncertainty about the specific mechanics of how angles and positions change due to length contraction, and there are unresolved questions regarding the conditions under which the triangle's properties may or may not hold.

djsourabh
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http://https://www.physicsforums.com/attachment.php?attachmentid=56297&stc=1&d=1362318192 problem:-
The situation is shown in attachment.
the right angled frame of rods (in stationary ) is moving at speed v perpendicular to its hypotenuse.
according to length contraction the corresponding lengths of sides should contract.
So it may not remain a right angled triangle in moving frame.
but if 'V' is such that L*cos(90-a) contracts such that L contracts than half of hypotenuse (h/2) .
we know that hypotenuse can not contract .
Also both L(AB) & L(AC) contract less than h/2. what happens in that case?
(L is the length of each side, consider isosceles triangle.
∠a is the angle opposite to point A)
 

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djsourabh said:
The situation is shown in attachment.
The attachment is missing.
 
i am trying to figure out why.
 
OK, in the meantime I will answer from what I can understand by your verbal description as much as possible. From your description it sounds like the hypotenuse is perpendicular to the direction of motion and the "legs" are each oblique to the direction of motion. For an oblique angle you can separate that into a parallel and perpendicular component. The perpendicular component will not length contract at all, only the parallel component. So no matter how great the length contraction you will always have a triangle (though not a right triangle).
 
thank you i got what you are trying to tell.
but i am not getting the reason why the lengths of sides should tilt towards hypotenuse as if they are going to coincide hypotenuse.why their position or angle should change?
and how?
 
Imagine, instead of a triangle, you have a series of rods of different lengths all stacked closely together. Each rod is oriented parallel to the direction of travel (perpendicular to the hypotenuse), the front ends are lined up with the hypotenuse, and the length of each rod is such that the back end lands on one of the legs of the triangle. So the outline of the stack of rods coincides with the triangle.

Now, each rod is going parallel to the direction of travel, so each one is contracted according to the standard length contraction formula. What is the resulting outline shape?
 
yes sir ,resulting locus is the sides of triangle.
thank you for your answers.
 

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