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Chapter 37: Q85P (page 1151)

One cosmic-ray particle approaches Earth along Earth鈥檚 north-south axis with a speed of 0.80ctoward the geographic north pole, and another approaches with a speed of 0.60c toward the geographic south pole (Fig. 37- 34). What is the relative speed of approach of one particle with respect to the other?

Short Answer

Expert verified

The speed of one particle relative to another is0.95c.

Step by step solution

01

Relativistic velocity addition:

Suppose an object is moving with the velocity u' with respect to S' frame, which is moving with the velocity v with respect to frame S then the velocity of the object u with respect to S frame is,

role="math" localid="1663136206277" u=u'+v1+u'vc2

02

Determine the relative velocity:

Let鈥檚 consider the rest frame of 0.6cparticle moving towards the south-pole to be Sframe. And the earth frame is called S'frame.

In S frame, earth is moving towards it with velocity v=0.6c and relative to this S' frame a particle is moving towards the North pole with speed u'=0.8c.

Then the velocity of this same particle relative to Sframe is,

u=0.8c+0.6c1+0.80.6=1.4c1.48=0.946c

Hence, the speed of one particle relative to other is 0.95c.

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Most popular questions from this chapter

Question: Apply the binomial theorem (Appendix E) to the last part of Eq. 37-52 for the kinetic energy of a particle. (a) Retain the first two terms of the expansion to show the kinetic energy in the form

K=(firstterm)+(secondterm)

The first term is the classical expression for kinetic energy. The second term is the first-order correction to the classical expression. Assume the particle is an electron. If its speed vis c/20, what is the value of (b) the classical expression and (c) the first-order correction? If the electron鈥檚 speed is 0.80s, what is the value of (d) the classical expression and (e) the first-order correction? (f) At what speed parameter 尾does the first-order correction become 10%or greater of the classical expression?

A sodium light source moves in a horizontal circle at a constant speed of 0.100c while emitting light at the proper wavelength of 位o=589nm. Wavelength 位is measured for that light by a detector fixed at the center of the circle. What is the wavelength shift 位-位o?

The length of a spaceship is measured to be exactly half its rest length. (a) To three significant figures, what is the speed parameter 尾of the spaceship relative to the observer鈥檚 frame? (b) By what factor do the spaceship鈥檚 clocks run slow relative to clocks in the observer鈥檚 frame?

The total energy of a proton passing through a laboratory apparatus is 10.611-nJ. What is its speed parameter 尾 ? Use the proton mass given in Appendix B under 鈥淏est Value,鈥� not the commonly remembered rounded number.

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=鈭�0.800c . What value will u'have if (a) v=0.80cand (b)v鈫�c ?
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