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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.

Grade:upto college level

1 Answers

Deepak Patra
askIITians Faculty 471 Points
8 years ago
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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