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Chapter 2: Q73E (page 67)
A spring has a force constant 18 N/m. If it is compressed 50 cm from its equilibrium length, how much mass will it have gained?
The gain in mass of spring is
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According to an observer at Earth's equator, by how much would his clock and one on a satellite in geosynchronous orbit differ in one day? (Geosynchronous orbit means an orbit period of one day-always in the same place in the sky)
A projectile is a distance r from the center of a heavenly body and is heading directly away. Classically, if the sum of its kinetic and potential energies is positive, it will escape the gravitational pull of the body, but if negative, it cannot escape. Now imagine that the projectile is a pulse of light energy E. Since light has no internal energy ,E is also the kinetic energy of the light pulse. Suppose that the gravitational potential energy of the light pulse is given by Newton鈥檚 classical formula U=-(GMm/r), where M is the mass of the heavenly body and m is an 鈥渆ffective mass鈥� of the light pulse. Assume that this effective mass is given by .
Show that the critical radius for which light could not escape the gravitational pull of a heavenly body is within a factor of 2 of the Schwarzschild radius given in the chapter. (This kind of 鈥渟emiclassical鈥� approach to general relativity is sometimes useful but always vague. To be reliable, predictions must be based from beginning to end on the logical, but unfortunately complex, fundamental equations of general relativity.)
A proton is accelerated from rest through a potential difference of
(a) What is its speed?
(b) Classical mechanics indicates that quadrupling the potential difference would double the speed. Were a classical analysis valid, what speed would result from a potential difference?
(c) What speed actually results?
By what factor would a star's characteristic wavelengths of light be shifted if it were moving away from Earth at ?
The light from galaxy NGC 221 consists of a recognizable spectrum of wavelengths. However, all are shifted towards the shorter-wavelength end of the spectrum. In particular, the calcium 鈥渓ine鈥� ordinarily observed at is observed at . Is this galaxy moving toward or away from Earth? At what speed?
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