Question

Hit the Ski Slopes EXAMPLE 5.8 GOAL Combine conservation of mechanical energy with the work-energy theorem involving friction on a horizontal surface. h = 20.0 m у A skier starts PROBLEM from rest at the top of a frictionless incline of height (В С) 20.0 m, as in the figure. At the bottom of the incline, the skier The skier slides down the slope and onto a level surface, stopping after encounters a horizontal traveling a distance d from the bottom of the hill. surface where the coefficient of kinetic friction between skis and snow is 0.210. (a) Find the skier's speed at the bottom. (b) How far does the skier travel on the horizontal surface before coming to rest? Neglect air resistance. STRATEGY Going down the frictionless incline is physically no different than going down a frictionless slide and is handled the same way, using conservation of mechanical energy to find the speed vB at the bottom. On the flat, rough surface, use the work-energy theorem with Wnc = Wfric = -fkd, where f is the magnitude of the force of friction and d is the distance traveled on the horizontal surface before coming to rest SOLUTION (A) Find the skier's speed at the bottom. Write down the equation for = 19.8 m/s Ув 3D V 2gh V2(9.80 m/s2)(20.0 m) conservation of energy, insert the values vA 0 and yB = 0, solve for vB and substitute values for g and yB as the skier moves from the top, point , to the bottom, point
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Answer 1

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W PEKE = PE tKE ini Elost Otmgh 2 m Vs t Fd A mahveg cose d 2 Vo 2 g h-ugdcose) h dsine 2(48x20-0222x98 cot20 xho) SinB 2 x G-&x20 (1- 0.222x cot 20) t2 5 2.903 Ve2 VB 2 36 5 m/s 2 Wnet = LmV-mva -Jmgd=mva 5 2.903 -0.210A 9-8 x d 2 d 37.148 m