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Chapter 36: Q. 14 (page 1059)

At what speed, as a fraction of c,does a moving clock tick at half the rate of an identical clock at rest?

Short Answer

Expert verified

At 0.866c, a moving clock tick at half the rate of an identical clock at rest.

Step by step solution

01

Given Information

We have to find the speed of the moving clock as a fraction ofc.

02

Simplify

The ticks that are being counted are those of a ticking clock. In S'-the time interval between two ticks is measured by the same clock, namely the ticking clock. As a result, 鈭�t'=鈭�蟿is the correct time. Between two ticks of the running clock, the rest clock measures a longer interval 鈭�t. These are linked by the following:

鈭�蟿=1-尾2鈭�t

Now 鈭�蟿=12鈭�t,Thus,

1-尾2=1-v2c2=12

v=c34v=0.866c

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