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Chapter 37: Q2Q (page 1144)

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 鈭�x'between the point at which the proton is fired and the point at which it hits the ship鈥檚 rear wall a positive or negative quantity? (b) Is the temporal separation 鈭�t'between those events a positive or negative quantity?

Short Answer

Expert verified

(a) The spatial separation 鈭�x'between the point at which the proton is fired and the point at which it hits the ship鈥檚 rear wall is anegative quantity.

(b) The temporal separation鈭�t' between those events is a positive.

Step by step solution

01

Write the given data from the question.

The proton is fired nearly speed of the light along the length of the ship.

02

Determine the spatial separation is the positive or negative quantity?

(a)

The spatial separation is defined as the separation between the two events is greater than speed of light, c times their time separation.

Since the given figure it can be seen that the spatial separation if directed toward the negative x axis, therefore, spatial separation is the negative quantity.

Hence the spatial separation鈭�x' between the point at which the proton is fired and the point at which it hits the ship鈥檚 rear wall a positive quantity.

03

Determine the temporal separation is positive or negative quantity?

(b)

When two observers move relative to each other and measure the time with respect to each other then measurement of the time would be different for both the observer and this time measurement is known as temporal separation.

Since the temporal separation is measure the time, therefore it is the positive quantity.

Hence the temporal separation鈭�t' between those events is a positive.

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Most popular questions from this chapter

Bullwinkle in reference frame S' passes you in reference frame S along the common direction of the x' and x axes, as in Fig. 37-9. He carries three meter sticks: meter stick 1 is parallel to the x' axis, meter stick 2 is parallel to the y' axis, and meter stick 3 is parallel to the z' axis. On his wristwatch he counts off 15.0 s, which takes 30.0 s according to you. Two events occur during his passage. According to you, event 1 occurs at x1=33.0mand t1=22.0ns, and event 2 occurs at x2=53.0mand t2=62.0ns. According to your measurements, what is the length of (a) meter stick 1, (b) meter stick 2, and (c) meter stick 3? According to Bullwinkle, what are (d) the spatial separation and (e) the temporal separation between events 1 and 2, and (f) which event occurs first?

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?

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鈭�t=t2-t1. What is the smallest value of 鈭�t for which observer S' will determine that the two flashes occur at the same x' coordinate?

In fig. 37-9, the origins of the two frames coincide at t=t'=0 and the relative speed is 0.950c. Two micrometeorites collide at coordinates x=100km and t=200渭s according to an observer in frame S. What are the (a) spatial and (b) temporal coordinate of the collision according to an observer in frame S' ?

Superluminal jets. Figure 37-29a shows the path taken by a knot in a jet of ionized gas that has been expelled from a galaxy. The knot travels at constant velocity v鈫� at angle胃 from the direction of Earth. The knot occasionally emits a burst of light, which is eventually detected on Earth. Two bursts are indicated in Fig. 37-29a, separated by timet as measured in a stationary frame near the bursts. The bursts are shown in Fig. 37-29b as if they were photographed on the same piece of film, first when light from burst 1 arrived on Earth and then later when light from burst 2 arrived. The apparent distanceD炉app traveled by the knot between the two bursts is the distance across an Earth-observer鈥檚 view of the knot鈥檚 path. The apparent timeT炉app between the bursts is the difference in the arrival times of the light from them. The apparent speed of the knot is then V炉app=D炉app/T炉app. In terms of v, t, and胃 , what are (a)D炉app and (b)T炉app ? (c) EvaluateV炉app forv=0.980c and 胃=30.0鈭�. When superluminal (faster than light) jets were first observed, they seemed to defy special relativity鈥攁t least until the correct geometry (Fig. 37-29a) was understood.
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