456 RelativityP39.69(a)At any speed, the momentum of the particle is given bypmumuuc==−γ12bg.Since FqEdpdt:qEddtmuuc=−FHGIKJLNMMOQPP−12212qEmucdudtmuucucdudtFHGIKJ+−FHGIKJFHGIKJ−−112122222322.SoqEmdudtuc uc=−+−LNMMMOQPPP1122 2222ejandadudtqEmuc−FHGIKJ122.(b)For usmall compared to c, the relativistic expression reduces to the classical aqEm=. As uapproaches c, the acceleration approaches zero, so that the object can never reach the speedof light.(c)duqEmdtutt100−=zz=uqEctmcqEt=+2 22xudtqEctdttt+00xcqEmc=+−FHIKP39.70(a)An observer at rest relative to the mirror sees the light travel a distance Ddx2, wherexvtS=is the distance the ship moves toward the mirror in time tS. Since this observeragrees that the speed of light is c, the time for it to travel distance DistDcdvtcSS−2tdcvS=+2.(b)The observer in the rocket measures a length-contracted initial distance to the mirror of
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .