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A 80kg skier grips a moving rope that is powered by an engine and is pulled at constant speed to the

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A 80

kg skier grips a moving rope that is powered by an engine and is pulled at constant speed to the top of a 22 hill. The skier is pulled a distance x = 200m along the incline and it takes 2.3min to reach the top of the hill
Nov 2nd, 2014

Since the skier is pulled at a constant speed, the pulling force (for one skier)is given by: 

F = m*g[sin theta + mu_k*cos theta] 
= 80*10[sin25+0.15*cos25] 
= 446.8N (along the incline upwards) 

Work done by F in moving distance of 230m: 
W=F*x = 446.8*230 =102,776 Joules 
Power reqd for this work: 
P= W/time = 102,776J/138s = 745 watts = 1HP(approx.) 
So for 30 skiers, engine power required = 30HP 

Nov 2nd, 2014

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Nov 2nd, 2014
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Nov 2nd, 2014
Jun 26th, 2017
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