A skier of mass 72 kg is pulled up a slope by a motor-driven cable. (a) How much

Question

A skier of mass 72 kg is pulled up a slope by a motor-driven cable. (a) How much work is required to pull him 85 m up a 30 degree slope (assumed frictionless) at a constant speed of 2.2 m/s? Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. (b) What power (expressed in hp) must a motor have to perform this task? Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. hp

Explanation / Answer

work done is calculated as follows:

W = mgdy

= mgdsin@

= 72*9.8*85*sin30o

= 29.988x103 J

= 29.988 kJ

= 30 kJ

(B)

Power is calculated as follows:

P = Fv

= mgsin@*v

= 72*9.8*85*sin30o*2.2

= 776.16 W

= 776.16 W [1 hP / 746 W]

= 1.04 hP

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