ch08-p088 - 88. (a) We take the gravitational potential...

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88. (a) We take the gravitational potential energy of the skier-Earth system to be zero when the skier is at the bottom of the peaks. The initial potential energy is U i = mgH , where m is the mass of the skier, and H is the height of the higher peak. The final potential energy is U f = mgh , where h is the height of the lower peak. The skier initially has a kinetic energy of K i = 0, and the final kinetic energy is Km v f = 1 2 2 , where v is the speed of the skier at the top of the lower peak. The normal force of the slope on the skier does no work and friction is negligible, so mechanical energy is conserved: 2 1 2 ii f f UKU K m g Hm g h m v += + ¡ =+ Thus, 2 2 ( ) 2(9.8m/s )(850 m 750 m) 44 m/s vg H h =− = −= . (b) We recall from analyzing objects sliding down inclined planes that the normal force
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