# Solution of Physics by Arthur Beiser

1. If the speed of light were smaller than it is, would relativistic phenomena be more or less conspicuous than they are now?

¡¼Sol¡½ All else being the same, including the rates of the chemical reactions that govern our brains and bodies, relativisitic phenomena would be more conspicuous if the speed of light were smaller. If we could attain the absolute speeds obtainable to us in the universe as it is, but with the speed of light being smaller, we would be able to move at speeds that would correspond to larger fractions of the speed of light, and in such instances relativistic effects would be more conspicuous.

3.

An athlete has learned enough physics to know that if he measures from the earth a time interval on a moving spacecraft, what he finds will be greater than what somebody on the spacecraft would measure. He therefore proposes to set a world record for the 100-m dash by having his time taken by an observer on a moving spacecraft. Is this a good idea?

¡¼Sol¡½ Even if the judges would allow it, the observers in the moving spaceship would measure a longer time, since they would see the runners being timed by clocks that appear to run slowly compared to the ship's clocks. Actually, when the effects of length contraction are included (discussed in Section 1.4 and Appendix 1), the runner's speed may be greater than, less than, or the same as that measured by an observer on the ground.

Inha University

Department of Physics

5.

Two observers, A on earth and B in a spacecraft whose speed is 2.00 x 108 m/s, both set their watches to the same time when the ship is abreast of the earth. (a) How much time must elapse by A's reckoning before the watches differ by 1.00 s? (b) To A, B's watch seems to run slow. To B, does A's watch seem to run fast, run slow, or keep the same time as his own watch?

¡¼Sol¡½ Note that the nonrelativistic approximation is not valid, as v/c = 2/3. (a) See Example 1.1. In Equation (1.3), with t representing both the time measured by A and the time as measured in A's frame for the clock in B's frame to advance by to, we need 2 2 1 − 1 − v = t 1 − 1 − 2 = t × 0.255 = 1.00 s t − t0 = t c2 3 from which t = 3.93 s. (b) A moving clock always seems to run slower. In this problem, the time t is the time that observer A measures as the time that B's clock takes to record a time change of to.

Inha University

Department of Physics

7.

How fast must a spacecraft travel relative to the earth for each day on the spacecraft to correspond to 2 d on the earth?

¡¼Sol¡½ From Equation (1.3), for the time t on the earth to correspond to twice the time t0 elapsed on the ship’s clock, v2 1 3 1 − 2 = , so v = c = 2.60 × 108 m/s, 2 2 c relating three significant figures. 9. A certain particle has a lifetime of 1.00 x10-7 s when measured at rest. How far does it go before decaying if its speed is 0.99c when it is created?

¡¼Sol¡½ The lifetime of the particle is t0, and the distance the particle will travel is, from Equation (1.3), vt = vt 0 1 − v /c 2 2

=

( 0.99)( 3.0 × 108 m/s)(1.00 × 10− 7 s) 1 − ( 0.99)

2

= 210 m

to two significant figures.

Inha University

Department of Physics

11. A galaxy in the constellation Ursa Major is receding from the earth at 15,000 km/s. If one of the characteristic wavelengths of the light the galaxy emits is 550 nm, what is the corresponding wavelength measured by astronomers on the earth? ¡¼Sol¡½ See Example 1.3; for the intermediate calculations, note that

c c νo 1 − v /c = = λo , ν νo ν 1 + v /c where the sign convention for v is that of Equation (1.8), which v positive for an approaching source and v negative for a receding source. For this problem, v 1.50 × 107 km/s =− = −0.050, c 3.0 × 108 m/s so that λ= λ = λo 1 − v /c 1 + 0.050 = (550 nm) = 578 nm 1 + v /c 1 − 0.050

Inha University

Department of Physics

13. A spacecraft receding from the...

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