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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鈥檚 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 尾for a range of values for 尾. 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 尾=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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Most popular questions from this chapter

You wish to make a round trip from Earth in a spaceship, traveling at constant speed in a straight line for exactly 6 months (as you measure the time interval) and then returning at the same constant speed. You wish further, on your return, to find Earth as it will be exactly 1000 years in the future. (a) To eight significant figures, at what speed parameter 尾must you travel? (b) Does it matter whether you travel in a straight line on your journey?

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