Please show EACH step without shortcuts! Explanations appreciated Problem #1 A s

Question

Please show EACH step without shortcuts! Explanations appreciated

Problem #1 A skier starts from rest at the top of a smooth incline of height 20 m as in Figure 1. At the bottom of the incline, the skier encounters a horizontal rough surface where the coefficient of kinetic friction between the skis and the snow is 0.21. (a) How far does the skier travel on the horizontal surface before coming to rest? (b) Find the horizontal distance the skier travels before coming to rest if the incline is also rough with a coefficient of kinetic friction equal to 0.21. Assume two significant digits. 20 m 20° Figure 1: See Problem #1

Explanation / Answer

(A) Applying work energy theorem,

Work done by gravity + work done by friction = change in KE

m g h - uk m g d = 0 - 0

d = h / uk = 20 / 0.21 = 95.2 m .............Ans

{ work done by friction = - fk . d and fk = uk N = uk m g}

(b) Work done by gravity + work done by friction = change in KE

m g h - (uk m g d + (uk m g cos20)(h/sin20)) = 0 - 0

h - uk d - uk h / tan20 = 0

d = (h/uk) - (h / tan20)

d = 40.3 m .............Ans

{ work done by friction on incline will also add.

W = - fk .d' and fk = uk N = uk m g cos20

and d'= h/sin20

so W = - uk m g h / tan20 }

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