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Chapter 37: 30P (page 1147)

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?

Short Answer

Expert verified

The multiple of c is 0.588.

Step by step solution

01

Describe the expression for the velocity of the particle

The relativistic velocity of the particle is given by,

u=u'+v1+u'vc …… (1)

Here, data-custom-editor="chemistry" u=0.400c is the velocity of stellar Q2 in reference frame, and data-custom-editor="chemistry" u=0.800c is the velocity of the reference frame of the observer on stellar Q1 relative to the reference frame.

02

Determine the multiple of c

Rearrange the equation (1) for u'.

u1+u'vc2=u'+vuu'vc-u'=v-uu'uvc2-1=v-uu'=v-uuvc2-1 …… (2)

Substitute 0.800c for v, and 0.400c for u in equation (2).

u'=0.800c-0.400c0.800c0.400cc2-1=0.400c0.32-1=-0.588c

Here, the negative sign indicates the opposite direction.

Therefore, the multiple of c is 0.588.

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Most popular questions from this chapter

In Fig. 37-28a, particle P is to move parallel to thex andx' axes of reference framesSand S', at a certain velocity relative to frame S. FrameS' is to move parallel to thex axis of frame Sat velocity v. Figure 37-28b gives the velocityu' of the particle relative to frameS' for a range of values forv . The vertical axis scale is set byu'a=−0.800c . What value will u'have if (a) v=0.80cand (b)v→c ?

In one year the United States consumption of electrical energy was about 2.2×1012kW.h.

(a) How much mass is equivalent to the consumed energy in that year?

(b) Does it make any difference to your answer if this energy is generated in oil-burning, nuclear, or hydroelectric plants?

Figure 37-20 shows the triangle of Fig 37-14 for six particles; the slanted lines 2 and 4 have the same length. Rank the particles according to (a) mass, (b) momentum magnitude, and (c) Lorentz factor, greatest first. (d) Identify which two particles have the same total energy. (e) Rank the three lowest-mass particles according to kinetic energy, greatest first.

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?

Another approach to velocity transformations. In Fig. 37-31, reference frames B and C move past reference frame A in the common direction of their xaxes. Represent the xcomponents of the velocities of one frame relative to another with a two-letter subscript. For example, vABis the xcomponent of the velocity of A relative to B. Similarly, represent the corresponding speed parameters with two-letter subscripts. For example, βAB(=vAB/c)is the speed parameter corresponding to vAB.

(a) Show thatβAC=βAB+βBC1+βABβBC

Let MABrepresent the ratio(1−βAB)/(1+βAB) , and letMBC andMAC represent similar ratios.

(b) Show that the relation

MAC=MABMBC

is true by deriving the equation of part (a) from it.
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