PS7 - In units of kilograms per minute, what is the rate that coal can be lifted from the mine?

Question

Coal is being lifted a vertical distance of 49.9 m from a mine by an engine that supplies 399 W of power.

Answer 1

Draw a free-body diagram.

We will assume that the coal is lifted at constant velocity meaning there is no acceleration. or that the sum of the forces in the y-direction is zero:

∑F_y = 0 = T - F_G where "T" is the tension in the rope and F_G is the force of gravity (or mass times "g")

T = mg

Let "m" be 1 kg

So T = (1)(9.8) or T = 9.8 N

The work done is T•d or (9.8)(49.9) = 489.02 Nm = 489.02 joules

Since power is energy divided by time (P = W/t) then 399 = 489.02/t then:

399t = 489.02

t = 489.02/399 = 1.2256 seconds

That would mean the rate is (1 kg)/(1.2256 seconds) = 0.816 kg/s

Converting to minutes:

(0.815 kg/s) x (60 s/min) = 49.0 kg/min