51. (a) The initial potential energy is Umgyii===×(5201kg) 9.8m s (300 m).53 10 J26diwhere +yis upward and y= 0 at the bottom (so that Uf= 0). (b) Since fk= μkFN= kmgcosθwe havethcoskkEfdmgdΔ==from Eq. 8-31. Now, the hillside surface (of length d= 500 m) is treated as an hypotenuse of a 3-4-5 triangle, so cos = x/dwhere x= 400 m. Therefore,
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