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Chapter 37: Q91P (page 1151)

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?

Short Answer

Expert verified

The speed of cruiser B such that cruiser A and station approaches it with same speed is 0.400c.

Step by step solution

01

Identification of given data

The relative speed of Cruiser A is vA=0.800c

The relative speed of cruiser A relative to B will be equal to the relative speed of cruiser B relative to station. The station is stationary so its speed will be zero relative to both cruisers.

02

Determination of speed of cruiser B

The speed of cruiser B is given as:

vs-vB=vB-vAvB=vs+vA2

Here, vs is the speed of station and its value is zero because both cruisers are at rest.

Substitute all the values in the above equation.

vB=0+0.800c2vB=0.400c

Therefore, the speed of cruiser B such that cruiser A and station approaches it with same speed is 0.400c.

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Most popular questions from this chapter

A radar transmitterTisfixedto a reference frame S'that is moving to the right with speed v relative to reference frame S(Fig. 37-33). A mechanical timer (essentially a clock) in frame S', having a period τ∘ (measured inS' ), causes transmitter Tto emit timed radar pulses, which travel at the speed of light and are received by R, a receiver fixed in frame S. (a) What is the period τof the timer as detected by observer A, who is fixed in frame S? (b) Show that at receiver R the time interval between pulses arriving fromT is not τor τo, but

τR=τoc+vc-v

(c) Explain why receiver Rand observer A, who are in the same reference frame, measure a different period for the transmitter. (Hint: A clock and a radar pulse are not the same thing.)

A pion is created in the higher reaches of Earth’s atmosphere when an incoming high-energy cosmic-ray particle collides with an atomic nucleus. A pion so formed descends toward Earth with a speed of 0.99c. In a reference frame in which they are at rest, pion decay with an average life of 26 ns. As measured in a frame fixed with respect to Earth, how far (on the average) will such a pion move through the atmosphere before it decays?

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?

Figure 37-16 shows a ship (attached to reference frame S') passing us (standing in reference frameS). A proton is fired at nearly the speed of light along the length of the ship, from the front to the rear. (a) Is the spatial separation ∆x'between the point at which the proton is fired and the point at which it hits the ship’s rear wall a positive or negative quantity? (b) Is the temporal separation ∆t'between those events a positive or negative quantity?

An electron of β=0.9999987moves along the axis of an evacuated tube that has a length of 3.00 m as measured by a laboratory observer S at rest relative to the tube. An observer S’ who is at rest relative to the electron, however, would see this tube moving with speed v ( =βC).What length would observer S’ measure for the tube?
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