Answered: An Other Frame moves with a speed of…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

An Other Frame moves with a speed of 0.80 relative to the Home Frame. An object at rest in the Other Frame has a length of 30 ns as measured in the Home Frame. What is the object's length in the Other Frame?

Expert Solution

Step 1: Length Contraction in Frame

The length contraction formula relates the length of an object in a moving frame (L) to its length in the rest frame ( $L subscript 0$ ) and the relative velocity (v) between the two frames:

$L equals L subscript 0 space square root of 1 minus v squared over c squared end root space$

Where: L = Length of the object in the moving frame (Other Frame)

$L subscript 0 space$ = Length of the object in the rest frame (Home Frame), here, $L subscript 0$ =30 ns (nanoseconds) = $3 cross times 10 to the power of negative 9 end exponent$ seconds

v = Relative velocity between the frames, here v = 0.80c (80% of the speed of light)

c = Speed of light in a vacuum (approximately 3.00 x 10^8 meters per second)

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