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Chapter 20: Problem 3

A rod lies parallel to the \(x\) axis of reference frame \(S\), moving along this axis at a speed of \(0.632 c .\) Its rest length is \(1.68 \mathrm{~m}\). What will be its measured length in frame \(S ?\)

Short Answer

Expert verified
The measured length of the rod in the frame S will be calculated using the steps provided above. As it is a numerical solution, the answer will be a precise numerical value (in metres).

Step by step solution

01

Identify given values

Identify the values given in the problem, which include: \n1. Speed of the rod (\(v\)) is \(0.632c\), where \(c\) is the speed of light. \n2. Rest length (\(L_0\)) is \(1.68m\).
02

Apply the length contraction formula

The formula for length contraction is \(L = L_0 \sqrt{1 - \frac{v^2}{c^2}}\). Substitute the given values into the formula.
03

Solve for \(L\)

Complete the substitution and simplify the expression to find the contracted length (L).

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