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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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Most popular questions from this chapter

The mean lifetime of stationary muons is measured to be 2.2000μs. The mean lifetime of high-speed muons in a burst of cosmic rays observed from Earth is measured to be 16.000μs. To five significant figures, what is the speed parameter βof these cosmic-ray muons relative to Earth?

In Fig. 37-36, two cruisers fly toward a space station. Relative to the station, cruiser A has speed 0.800c. Relative to the station, what speed is required of cruiser B such that its pilot sees A and the station approach B at the same speed?

Figure 37-18 shows two clocks in stationary frame S(they are synchronized in that frame) and one clock in moving frame S'.Clocks C1and C'1read zero when they pass each other. When clocks C1and C2pass each other, (a) which clock has the smaller reading and (b) which clock measures a proper time?

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