236 Potential EnergyAdditional ProblemsP8.48The potential energy of the block-Earth system is mgh.An amount of energy µθkmgdcos is converted into internal energy due to friction on the incline.Therefore the final height ymaxis found frommgymghmgdkmaxcos=−wheredymgymghmgyk=∴=−maxmaxmaxsincotθSolving,yhkmaxcot=+1.ymaxhFIG. P8.48P8.49At a pace I could keep up for a half-hour exercise period, I climb two stories up, traversing fortysteps each 18 cm high, in 20 s. My output work becomes the final gravitational energy of the systemof the Earth and me,mgy=×=859 8040 0 186 000kgm smJ2bgejaf..making my sustainable power 6000102J20 sW=~.P8.50v==10027 8km hm s.The retarding force due to air resistance isRDAv=12120330 120250
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