Classical dynamics greenwood solution manual

In its own frame of reference, a proton takes 5 min to cross the Milky Way galaxy, which is about 105 light-years in diameter. In Equation (1.4), we have v = 0 and V = -u, where u is the speed of the spacecraft, moving away from the earth (V > Elc2) and t в‰€ L/c. гЂђSolгЂ‘ This problem may be done in several ways, all of which need to use the fact that when the frequencies due to the classical and relativistic effects are found, those frequencies, while differing by 1 Hz, will both be sufficiently close to vo = 109 Hz so that vo could be used for an approximation to either. If the receiver on earth can measure frequencies to the nearest hertz, at what spacecraft speed can the difference between the relativistic and classical Doppler effects be detected? For the classical effect, assume the earth is stationary. A spacecraft receding from the earth emits radio waves at a constant frequency of 109 Hz. 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? гЂђSolгЂ‘ See Example 1.3 for the intermediate calculations, note thatД¬ c ОЅo 1 в€’ v /c = О»o, ОЅ ОЅo ОЅ 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. A galaxy in the constellation Ursa Major is receding from the earth at 15,000 km/s. гЂђSolгЂ‘ The lifetime of the particle is t0, and the distance the particle will travel is, from Equation (1.3), vt = How far does it go before decaying if its speed is 0.99c when it is created?

9.ДЄ certain particle has a lifetime of 1.00 x10-7 s when measured at rest. гЂђSolгЂ‘ From Equation (1.3), for the time t on the earth to correspond to twice the time t0 elapsed on the shipвЂ™s clock, v2 1 3 1 в€’ 2 =, so v = c = 2.60 Г— 108 m/s, 2 2 c relating three significant figures.

How fast must a spacecraft travel relative to the earth for each day on the spacecraft to correspond to 2 d on the earth? 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. (b) A moving clock always seems to run slower. 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 2пЈ¶ пЈ« пЈ« v 2 пЈ¶пЈ· пЈ« 2пЈ¶ пЈ· пЈ¬ пЈ¬ t в€’ t 0 = t 1 в€’ 1 в€’ 2 = t 1 в€’ 1 в€’ пЈ¬ пЈ· = t Г— 0.255 = 1.00 s пЈ¬ пЈ¬ c пЈ·пЈё пЈ 3пЈё пЈ· пЈ пЈ пЈё from which t = 3.93 s. гЂђSolгЂ‘ Note that the nonrelativistic approximation is not valid, as v/c = 2/3. To B, does A's watch seem to run fast, run slow, or keep the same time as his own watch? (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. 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. 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. гЂђSolгЂ‘ 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.

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

Classical dynamics greenwood solution manual