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Chapter 37: Q14P (page 1146)

A rod is to move at constant speed v along the xaxis of reference frame S, with the rod’s length parallel to that axis. An observer in frame Sis to measure the length Lof the rod. Figure 37-23 given length Lversus speed parameter βfor a range of values for β. The vertical axis scale is set by La=1.00m. What is L if v=0.95c?

Short Answer

Expert verified

The value of L is 0.25 .

Step by step solution

01

The relation between lengths in different frames

The formula to find the length of the object in a reference frame is given by

L=L01-vc2.

02

The length of the rod

From the graph, it is clear that when β=0,L0=0.8 , and the value of v is 0.95c.

Substitute the known values and solve for L as follows:

L=L01-vc2L=0.81-0.95c2L=0.81-0.952L=0.25

Thus, the value of L is 0.25m .

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