ism_chapter_39 - Chapter 39 Relativity Conceptual...

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1301 Chapter 39 Relativity Conceptual Problems *1 Picture the Problem The total relativistic energy E of a particle is defined to be the sum of its kinetic and rest energies. The total relativistic energy of a particle is given by: 2 2 2 1 2 mc mu mc K E + = + = and correct. is ) ( a *2 Determine the Concept The gravitational field of the earth is slightly greater in the basement of the office building than it is at the top floor. Because clocks run more slowly in regions of low gravitational potential, clocks in the basement will run more slowly than clocks on the top floor. Hence, the twin who works on the top floor will age more quickly. correct. is ) ( b 3 ( a ) True ( b ) True ( c ) False. The shortening of the length of an object in the direction in which it is moving is independent of the velocity of the frame of reference from which it is observed. ( d ) True ( e ) False. Consider two explosions equidistant, but in opposite directions, from an observer in the observer’s frame of reference. ( f ) False. Whether events appear to be simultaneous depends on the motion of the observer. ( g ) True 4 Determine the Concept Because the clock is moving with respect to the first observer, a time interval will be longer for this observer than for the observer moving with the spring-and-mass oscillator. Hence, the observer moving with the system will measure a
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Chapter 39 1302 period that is less than T. correct. is ) ( b 5 Determine the Concept Although y = y , t ≠∆ t . Consequently, u y = y / t y / t = u y . Estimation and Approximation 6 •• Picture the Problem We can calculate the sun’s loss of mass per day from the number of reactions per second and the loss of mass per reaction. Express the rate at which the sun loses mass: m N t M = where N is the number of reactions per second and m is the loss of mass per reaction. Solve for M : t m N M = (1) Find the number of reactions per second, N : 1 38 19 26 s 10 eV J 10 1.60 reaction MeV 25 J/s 10 4 reaction / = × × × = = E P N The loss of mass per reaction m is: () kg 10 44 . 4 m/s 10 3 eV J 10 1.60 reaction MeV 25 reaction / 29 2 8 19 2 × = × × × = = c E m Substitute numerical values in equation (1) and evaluate M : ( ) ( )( ) kg 10 84 . 3 ks/d 4 . 86 d 1 kg 10 44 . 4 s 10 14 29 1 38 × = × = M
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Relativity 1303 *7 •• Picture the Problem We can use the result from Problem 30, for light that is Doppler- shifted with respect to an observer, + = 1 1 2 2 u u c v , where u = z + 1 and z is the red-shift parameter, to find the ratio of v to c . In ( b ) we can solve Hubble’s law for x and substitute our result from ( a ) to estimate the distance to the galaxy. ( a ) Use the result of Problem 30 to express v / c as a function of z : ( ) () 1 1 1 1 2 2 + + + = z z c v Substitute for z and evaluate v / c : ( ) 946 . 0
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ism_chapter_39 - Chapter 39 Relativity Conceptual...

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