# Chap 39 SM - Chapter 39 Relativity Conceptual Problems...

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239 Chapter 39 Relativity Conceptual Problems 1 [SSM] The approximate total energy of a particle of mass m moving at speed u << c is ( a ) mc 2 + 1 2 mu 2 , ( b ) 1 2 2 , ( c ) cmu , ( d ) mc 2 , ( e ) 1 2 cmu . Determine the Concept The total relativistic energy E of a particle is defined to be the sum of its kinetic and rest energies. The sum of the kinetic and rest energies of a particle is given by: 2 2 2 1 2 mc mu mc K E + = + = and ) ( a is correct. 2 A set of twins work in an office building. One twin works on the top floor and the other twin works in the basement. Considering general relativity, which twin will age more quickly? ( a ) They will age at the same rate. ( b ) The twin who works on the top floor will age more quickly. ( c ) The twin who works in the basement will age more quickly. ( d ) It depends on the speed of the office building. ( e ) None of the above. Determine the Concept The gravitational field of 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. ) ( b is correct. 3 True or false: ( a ) The speed of light is the same in all reference frames. ( b ) The time interval between two events is never shorter than the proper time interval between the two events. ( c ) Absolute motion can be determined by means of length contraction. ( d ) The light-year is a unit of distance. ( e ) Simultaneous events must occur at the same place. ( f ) If two events are not simultaneous in one frame, they cannot be simultaneous in any other frame. ( g ) The mass of a system that consists of two particles that are tightly bound together by attractive forces is less than the sum of the masses of the individual particles when separated. ( a ) True

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Chapter 39 240 ( 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 An observer sees a system moving past her that consists of a mass oscillating on the end of a spring and measures the period T of the oscillations. A second observer, who is moving with the mass–spring system, also measures its period. The second observer will find a period that is ( a ) equal to T , ( b ) less than T , ( c ) greater than T , ( d ) either ( a ) or ( b ) depending on whether the system was approaching or receding from the first observer, ( e ) Not enough information is given to answer the question.
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Chap 39 SM - Chapter 39 Relativity Conceptual Problems...

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