# Calculate the power of an electric engine which can life 20 ton of coal per hour from a mine 180 metre depth.

2
by kaushikabhi

2014-10-05T20:50:44+05:30

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Mass = 20,000kg
weight (F)= 20,000 × 10 N = 2×10⁵ N
depth = 180m
time = 1hr =3600s
velocity = 180/3600 = 0.05m/s

Power = force×velocity = 2×10⁵×0.05 = 10000 W = 10kW
2014-10-06T06:52:17+05:30

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I take a ton as a metric ton or tonne equal to 1000 kg weight.
mass of coal transported to a height of 180 meters in one hour
= 20 metric tons = 20,000 kg

Change in the potential energy of coal : m g h
= 20,000 kg * 9.81 m/sec² * 180 m = 35,316 kJoules

Power supplied by the electric engine = Energy supplied / time duration
= 35,316 kJ / 3600 sec = 9.81 kW

Power = 10 kW if g is taken as 10 m/sec²