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Chapter 37: 6P (page 1145)

Reference frame S’ is to pass reference frame S at speed v along the common direction of the and x axes, as in Fig. 37-9. An observer who rides along with frame S’ is to count off a certain time interval on his wristwatch. The corresponding time interval ∆t is to be measured by an observer in frame S. Figure 37-22 gives ∆tversus speed parameter βfor a range of values for . The vertical axis scale is set by ta 14.0 s. What is interval ∆t if v = 0.98c?

Short Answer

Expert verified

The time interval for observer is 40s.

Step by step solution

01

Identification of given data

The speed of reference frame S’ is v=0.98c

The duration for the reference frame S’ is t=8s

The time dilation is used to find the duration for particle before decay from detector.

02

Determination of time interval for observer

The time interval for observer is given as:

∆t=t1-vc2

Here, cis the speed of light and its value is 3×108m/s.

Substitute all the values in equation.

∆t=8s1-0.98cc2∆t=40s

Therefore, the time interval for observer is 40 s .

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Most popular questions from this chapter

What is the speed parameter for the following speeds: (a) a typical rate of continental drift (1 in./y); (b) a typical drift speed for electrons in a current-carrying conductor (0.5 mm/s); (c) a highway speed limit of 55 mi/h; (d) the root-mean-square speed of a hydrogen molecule at room temperature; (e) a supersonic plane flying at Mach 2.5 (1200 km/h); (f) the escape speed of a projectile from the Earth’s surface; (g) the speed of Earth in its orbit around the Sun; (h) a typical recession of a distant quasar due to the cosmological expansion 3×104kms-1.

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’s speed is 0.80s, what is the value of (d) the classical expression and (e) the first-order correction? (f) At what speed parameter βdoes the first-order correction become 10%or greater of the classical expression?

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.

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?
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