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Chapter 37: 6P (page 1145)

Reference frame S’ is to pass reference frame S at speed v along the common direction of the and x axes, as in Fig. 37-9. An observer who rides along with frame S’ is to count off a certain time interval on his wristwatch. The corresponding time interval ∆t is to be measured by an observer in frame S. Figure 37-22 gives ∆tversus speed parameter βfor a range of values for . The vertical axis scale is set by ta 14.0 s. What is interval ∆t if v = 0.98c?

Short Answer

Expert verified

The time interval for observer is 40s.

Step by step solution

01

Identification of given data

The speed of reference frame S’ is v=0.98c

The duration for the reference frame S’ is t=8s

The time dilation is used to find the duration for particle before decay from detector.

02

Determination of time interval for observer

The time interval for observer is given as:

∆t=t1-vc2

Here, cis the speed of light and its value is 3×108m/s.

Substitute all the values in equation.

∆t=8s1-0.98cc2∆t=40s

Therefore, the time interval for observer is 40 s .

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Most popular questions from this chapter

Stellar system Q1 moves away from us at a speed of 0.800c. Stellar system Q2, which lies in the same direction in space but is closer to us, moves away from us at speed 0.400c. What multiple of c gives the speed of Q2 as measured by an observer in the reference frame of Q1?

Figure 37-21 shows one of four star cruisers that are in a race. As each cruiser passes the starting line, a shuttle craft leaves the cruiser and races toward the finish line. You, judging the race, are stationary relative to the starting and finish lines. The speeds vc of the cruisers relative to you and the speeds of the shuttle craft relative to their respective starships are, in that order, (1) 0.70c, 0.40c; (2) 0.40c, 0.70c; (3) 0.20c, 0.90c; (4) 0.50c, 0.60c. (a) Rank the shuttle craft according to their speeds relative to you, greatest first. (b) Rank the shuttle craft according to the distances their pilots measure from the starting line to the finish line, greatest first. (c) Each starship sends a signal to its shuttle craft at a certain frequency f0 as measured on board the starship. Rank the shuttle craft according to the frequencies they detect, greatest first.

In Fig. 37-9, observer S detects two flashes of light. A big flash occurs at x1=1200mand , slightly later, a small flash occurs at x2=480m. The time interval between the flashes is∆t=t2-t1. What is the smallest value of ∆t for which observer S' will determine that the two flashes occur at the same x' coordinate?


The premise of the Planet of the Apes movies and books is that hibernating astronauts travel far into Earth’s future, to a time when human civilization has been replaced by an ape civilization. Considering only special relativity, determine how far into Earth’s future the astronauts would travel if they slept for 120 y while traveling relative to Earth with a speed of 0.9990c, first outward from Earth and then back again?

The plane of clocks and measuring rods in Fig. 37-19 is like that in Fig. 37-3. The clocks along the x axis are separated (center to center) by 1light-second, as are the clocks along the y axis, and all the clocks are synchronized via the procedure described in Module 37-1. When the initial synchronizing signal of t = 0 from the origin reaches (a) clock A, (b) clock B, and (c) clock C, what initial time is then set on those clocks? An event occurs at clock A when it reads 10 s. (d) how long does the signal of that event take to travel to an observer stationed at the origin? (e) What time does that observer assign to the event?
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