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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鈥檚 Lorentz factor. (b) What time does the clock read as it passes x=180鈥尘?

Short Answer

Expert verified
  1. The clock鈥檚 Lorentz factor is 1.25.
  2. The clock reads 8.00脳10鈭�7s as it passes x=180鈥尘.

Step by step solution

01

The Lorentz factor

The formula of the Lorentz factor is 纬=11鈭�尾2, where尾 is the speed parameter.

02

Find Lorentz factor

(a)

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

The Lorentz factor can be calculated as follows:

纬=11鈭�尾2=11鈭�(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鈥尘in the unprimed frame is given by:

t=xv=1800.600(3.00脳108鈥尘/s)=1.00脳10鈭�6鈥塻

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

t'=t纬=1.00脳10鈭�61.25=8.00脳10鈭�7鈥塻

Thus, the reading on the clock is 8.00脳10鈭�7鈥塻.

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Most popular questions from this chapter

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