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Chapter 36: Q. 21 (page 1059)

At what speed, as a fraction of c, will a moving rod have a length60% that of an identical rod at rest?

Short Answer

Expert verified

The speed is0.8c.

Step by step solution

01

Given Information

We need to find the peed, as a fraction of c, will a moving rod have a length 60%that of an identical rod at rest.

02

Simplify

The moving rod is the frameS'and the ground frame is S.The length of rod is S'is the proper length lbecause the rod is at rest is S'.

L=1-β2l

The length is calculated to 60%when

L=0.6l1-β2=1-v2c2=0.6v=0.8c

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Most popular questions from this chapter

You are standing at x=9.0kmand your assistant is standing at x=3.0km.Lightning bolt 1strikes at x=0kmand lightning bolt 2strikes at x=12.0km.You see the flash from bolt 2at t=10μsand the flash from bolt 1att=50μs. According to your assistant, were the lightning strikes simultaneous? If not, which occurred first, and what was the time difference between the two?

a. Derive a velocity transformation equation for uyand uy'. Assume that the reference frames are in the standard orientation with motion parallel to the x- and x′-axes.

b. A rocket passes the earth at 0.80c. As it goes by, it launches a projectile at 0.60c perpendicular to the direction of motion. What is the particle’s speed, as a fraction of c, in the earth’s reference frame?

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a. Do the light fleshes reach the rocket pilot simultaneously? If not, which reaches her first? Explain

b. A student was sitting on the ground halfway between the trees as the rocket passed overhead. According to the student, were the lightning strikes simultaneous? If not, which tree was hit first? Explain.

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