What should be the power of an engine required to lift 90 metric tonnes of coal per hour from a mine whose depth is 200m?

Explanation

Here, mass of the coal to be lifted,
m = 90 metric tonnes ` = 9 xx 10^(4) kg`
Height through which the coal is to be lifted , h = 200 m
Time during which the coal is to be lifted,
`t = 1 h = 60 xx 60 = 3600 `
Work done to lift the coal,
`W = mgh = (9 xx 10 ^(4) kg) ( 10 m s^(-2)) (200 m)`
`= 1 . 8 xx 10 ^(8) J`
Power of the engine required,
`P = (W)/(t) = (1 . 8 xx 10 ^(8) J)/( 3600 s) = 50000 W = 50 k W `