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Chapter 37: Q23P (page 1147)

A clock moves along an xaxis at a speed of0.600c and reads zero as it passes the origin of the axis. (a) Calculate the clock’s Lorentz factor. (b) What time does the clock read as it passes x=180 m?

Short Answer

Expert verified
  1. The clock’s Lorentz factor is 1.25.
  2. The clock reads 8.00×10−7s as it passes x=180 m.

Step by step solution

01

The Lorentz factor

The formula of the Lorentz factor is γ=11−β2, whereβ is the speed parameter.

02

Find Lorentz factor

(a)

Here, given that v=0.600c. So, the speed parameter becomes β=vc=0.600.

The Lorentz factor can be calculated as follows:

γ=11−β2=11−(0.600)2=1.25

Thus, the value of Lorentz factor of the clock is 1.25.

03

The reading in the clock

(b)

The time reading in the clock to travel from the origin to x=180 min the unprimed frame is given by:

t=xv=1800.600(3.00×108 m/s)=1.00×10−6 s

Here, the reading is taken by the clock itself between two events. So, the reading on the clock at x=180is:

t'=tγ=1.00×10−61.25=8.00×10−7 s

Thus, the reading on the clock is 8.00×10−7 s.

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