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Problem 6: To what height can a 400 w engine lift a 100 kg mass in 3 s?

Solution

Given

Power of the engine, P = 400 W

Mass of the load, m = 100 kg

Time taken, t = 3 s

Required

Height of the load, h

When the load is lifted, work is done on it which stores in the body as its gravitational potential energy. If we ignore other factors, like air resistance, the work done will be equal to the gravitational potential energy of the body at the height. So work can be calculated by finding the P.E of the body and since power is rate of work done, therefore, using these two concepts the height h can be calculated as below.

Now, the work done by the engine, W = mgh ——- (1)
Similarly, power of the engine, P = W/t &Rightarrow; W = P × t —— (2)
Compare (1) and (2)
mgh = P × t
Put the values,
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