How long would the meter stick in the question 1 appear to be if it were traveling with its length perpendicular to its direction of motion? (Why is your answer different from your answer to the question 1?) Question 1 How long would a meterstick appear to be if it were traveling like a properly thrown spear at 99.5% the speed of light?
Solution 26RQ Introduction: In relativistic speeds, the length of an object is appeared to decreased when the observer or the object is travelling at non-zero velocity. This phenomenon is called as “length contraction” L = L 1 v2 The mathematical expression for length contraction is, 0 c2 Where, L - Length observed by the observer L0 Original length v - Relative speed between the observer and object c - Speed of light Step 1: Figure 1, clearly represents the alignment of the stick in question 1. The direction of motion of the moving frame and direction of motion of the stick were same. Hence, the contraction happens only in one direction that is, about the direction of motion of the frame. So, the stick’s length is appeared as contracted when it is moving with a relativistic speed of 99.5 % speed of light. In figure 2, the length is perpendicular to the direction of motion. The contraction will take place only in one direction. That is, the contraction will take place about the direction of motion. So, the length will not get affected but, the width do. Since the length is not affected, the length of the stick will be 1 metre itself when it is travelling with length perpendicular to the direction of motion independent of the speed. Conclusion: Length contraction will take place only in one direction and it will be about the direction of motion of the frame.