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In a 100-person ski lift, a machine raises passengers averaging 667 N in weight a height of 152 m in 55.0 s, at constant speed. Find the power output of the motor, assuming no frictional losses. In a 100-person ski lift, a machine raises passengers averaging 667 N in weight a height of 152 m in 55.0 s, at constant speed. Find the power output of the motor, assuming no frictional losses.
To obtain power (P), substitute mgh for W in the equation P = W/t,P = W/t = mgh/t …… (3)Since in a ski lift, there are 100-person and the machine raises passengers averaging 667 N in weight a height of 152 m in 55.0 s, at constant speed, therefore the power output of the motor will be,P = W/t = mgh/t = (100×667 N) h/t …… (4)To obtain power (P), substitute 152 m for h and 55.0 s for t in equation P=(100×667 N) h/t,P= (100×667 N) h/t = (100×667 N) (152 m)/(55.0 s) =1.84×105 N. m/s= (1.84×105 N. m/s) (1 W/ 1N. m/s)= 1.84×105 W …… (5)From the above observation we conclude that, the power output of the motor would be 1.84×105 W.
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