A sand mover at a quarry lifts 2,000 kg of sand per minute avertical distance of

Question

A sand mover at a quarry lifts 2,000 kg of sand per minute avertical distance of 12 meters. The sand is initially at rest andis discharged at the top of the sand mover with speed 5 m/s into aloading chute. At what minimum rate must power be supplied to thismachine? I know the answer is 4.34 kw but I don't know how to reachthat answer. Power=work/time it's ok if you don't understand my question because I alreadyhad my exam but thank you. A sand mover at a quarry lifts 2,000 kg of sand per minute avertical distance of 12 meters. The sand is initially at rest andis discharged at the top of the sand mover with speed 5 m/s into aloading chute. At what minimum rate must power be supplied to thismachine? I know the answer is 4.34 kw but I don't know how to reachthat answer. Power=work/time it's ok if you don't understand my question because I alreadyhad my exam but thank you.

Explanation / Answer

Given that            m =2000 kg            vf = 5m/s            t = 1min = 60 s            g =9.8 m/s2            h = 12m Work done = total change kinetic energy                   = 0.5 m ( vf2 - vi2)                    = 0.5 m ( vf2 - 2 (-g) h)         ( where initialspeed vi = 2g h )                    = 0.5 * 2000 * (25 - 2 * (-9.8) * 12 )    = 260200 J Power = W / t            = 260200 / 60            = 4.336 k            = 4.34 k

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