3. A few years ago, a group of miners was trapped 800 m below the surface. A res

Question

3. A few years ago, a group of miners was trapped 800 m below the surface. A rescue tunnel was dug down to thern and the miners were pulled up one at a time using a closed capsule to keep them safe from debris. The actual rescue tunnel was not exactly straight, and made some turns, but for this problem let's assume the tunnel is exactly straight and makes the 30° angle shown in the figure. Assume the mass of the capsule with one miner inside is 250 kg. Also, assume we have no friction between the capsule and the walls of the rescue tunnel (maybe we're using frictionless wheels or something...) It took 30 minutes (1800 sec) to pull each miner from the bottom to the top, and you can assume that the capsule is moving at a constant speed. 3o2> (a) How powerful did the motor have to be to do this? hp

Explanation / Answer

power = work done / time taken

= mgh/t

= 250*9.8*800/1800 = 1088.889 W

= 1088.88/745.7 hp = 1.46 hp answer

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