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Chapter 6: Q10E (page 1248)

A meter stick moves past you at great speed. Its motion relative to you is parallel to its long axis. If you measure the length of the moving meter stick to be 1.00 ft =0.3048m, 鈥攆or example, by comparing it to a 1-foot ruler that is at rest relative to you鈥攁t what speed is the meter stick moving relative to you?

Short Answer

Expert verified

The clock on the spacecraft shows the smaller elapsed time, and the difference in time is 1.12 h

Step by step solution

01

Concept of the time dilation equation.

The time dilation equation is given as螖迟=纬螖迟0/1-u2/c2whererole="math" localid="1664087018015" 鈭�t0 is the proper time in the rest frame,螖迟is the time interval measured in the second frame of reference u is the speed of the second frame with respect to the rest frame, c is the speed of light

02

Calculate the speed

An observer on the spacecraft measures the proper time螖迟0 which is given by equation

鈭�t0=鈭�t01-u2c2鈭�t0=鈭�t1-u2c2鈭�t0=鈭�t1-4.80脳10623脳1082=8758.88h

Hence, 螖迟-t0=1.12hthe clock on the spacecraft shows the smaller elapsed time

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