Chapter 10319P10.84(a)The mass of the roll decreases as it unrolls. We have mMrR=22where Mis the initial mass ofthe roll. Since ∆E=0, we then have ∆∆∆UKKg++=transrot0. Thus, when Imr=22,mgrMgRmvmr−++LNMOQP=bg22220ωSince rv=, this becomes vgRrr=−43332ej(b)Using the given data, we find v=×531 104. ms(c)We have assumed that ∆E=0. When the roll gets to the end, we will have an inelasticcollision with the surface. The energy goes into internal energy . With the assumption wemade, there are problems with this question. It would take an infinite time to unwrap the
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