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Chapter 37: Q6Q (page 1144)

Sam leaves Venus in a spaceship headed to Mars and passes Sally, who is on Earth, with a relative speed of 0.5c . (a) Each measures the Venus–Mars voyage time. Who measures a proper time: Sam, Sally, or neither? (b) On the way, Sam sends a pulse of light to Mars. Each measures the travel time of the pulse. Who measures a proper time: Sam, Sally, or neither?

Short Answer

Expert verified

(a) The Sam measures the proper time.

(b) Neither, Same nor sally can’t measure the proper time.

Step by step solution

01

Write the given data from the question.

Sam leaves Venus headed to Mars.

The relative speed of the sally is 0.5c.

02

Determine who measures the proper time for Venus- mars voyage time.

(a)

Sam is moving from Venus to mars;therefore, he can measure the time of the whole trip by using only one clock but sally is stationary on the earth, therefore she required two clocks to measure the complete time, one clock which measures the time for counting on Venus and other for stopping count on Mars.

Hence Sam measures the proper time.

03

Determine who measures the proper time when Sam sendsa pulse of light to Mars.

(b)

Since Sam and Sally are stationary relative to the light beam and their relative speed is the same which is 0.5c. Therefore, they cannot measure the time by using a single clock.

Hence neither Same nor sally can’t measure the proper time.

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Most popular questions from this chapter

A meter stick in frame S' makes an angle of 30owith the x’ axis. If that frame moves parallel to the x-axis of frame Swith speed 0.90c relative to frame S, what is the length of the stick as measured from S ?

Question:As you read this page (on paper or monitor screen), a cosmic ray proton passes along the left–right width of the page with relative speed v and a total energy of 14.24 nJ. According to your measurements, that left–right width is 21.0 cm. (a) What is the width according to the proton’s reference frame? How much time did the passage take according to (b) your frame and (c) the proton’s frame?

In Fig. 37-35, three spaceships are in a chase. Relative to an x-axis in an inertial frame (say, Earth frame), their velocities are vA=0.900c, vB, and vc=0.900c. (a) What value of vBis required such that ships A and C approach ship B with the same speed relative to ship B, and (b) what is that relative speed?

A particle with mass m has speed c/2 relative to inertial frame S. The particle collides with an identical particle at rest relative to frame S. Relative to S, what is the speed of a frame S’ in which the total momentum of these particles is zero? This frame is called the center of the momentum frame.

The car-in-the-garage problem. Carman has just purchased the world’s longest stretch limo, which has a proper length of Lc=30.5 m. In Fig. 37-32a, it is shown parked in front of a garage with a proper length of Lg=6.00 m. The garage has a front door (shown open) and a back door (shown closed).The limo is obviously longer than the garage. Still, Garageman, who owns the garage and knows something about relativistic length contraction, makes a bet with Carman that the limo can fit in the garage with both doors closed. Carman, who dropped his physics course before reaching special relativity, says such a thing, even in principle, is impossible.

To analyze Garageman’s scheme, an xc axis is attached to the limo, with xc=0 at the rear bumper, and an xg axis is attached to the garage, with xg=0 at the (now open) front door. Then Carman is to drive the limo directly toward the front door at a velocity of 0.9980c(which is, of course, both technically and financially impossible). Carman is stationary in the xcreference frame; Garageman is stationary in the role="math" localid="1663064422721" Xgreference frame.

There are two events to consider. Event 1: When the rear bumper clears the front door, the front door is closed. Let the time of this event be zero to both Carman and Garageman: tg1=tc1=0. The event occurs at xg=xc=0. Figure 37-32b shows event 1 according to the xg reference frame. Event 2: When the front bumper reaches the back door, that door opens. Figure 37-32c shows event 2 according to the xg reference frame.

According to Garageman, (a) what is the length of the limo, and what are the spacetime coordinates (b) xg2 and (c) tg2 of event 2? (d) For how long is the limo temporarily “trapped” inside the garage with both doors shut? Now consider the situation from the xc reference frame, in which the garage comes racing past the limo at a velocity of −0.9980c. According to Carman, (e) what is the length of the passing garage, what are the spacetime coordinates (f) Xc2and (g) tc2 of event 2, (h) is the limo ever in the garage with both doors shut, and (i) which event occurs first? (j) Sketch events 1 and 2 as seen by Carman. (k) Are the events causally related; that is, does one of them cause the other? (l) Finally, who wins the bet?
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