436 RelativityP39.2(a)vvvTB=+=60 0. m s(b)vvvTB=−=20 0. m s(c)vvvTB=+=+=2222204044 7. m sP39.3The first observer watches some object accelerate under applied forces. Call the instantaneousvelocity of the object v1. The second observer has constant velocity v21relative to the first, andmeasures the object to have velocity vvv2121=−.The second observer measures an acceleration ofavv221==ddtddt.This is the same as that measured by the first observer. In this nonrelativistic case, they measure thesame forces as well. Thus, the second observer also confirms that Fa∑=m.P39.4The laboratory observer notes Newton’s second law to hold:Fa11=m(where the subscript 1 implies the measurement was made in the laboratory frame of reference). Theobserver in the accelerating frame measures the acceleration of the mass asaaa21=−′(where the subscript 2 implies the measurement was made in the accelerating frame of reference,and the primed acceleration term is the acceleration of the accelerated frame with respect to the
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