Two identical $3-$in$.$ major$-$diameter power screws $($single$-$threaded$)$ with modified square

threads are used to raise and lower a $50-$ton sluice gate of a dam. Quality of construction and

maintenance $($including lubrication$)$ are good, resulting in an estimated friction coefficient of

only $0\mathrm{.}1$ for the screw. Collar friction can be neglected, as ball thrust bearings are used.

Assuming that, because of gate friction, each screw must provide a lifting force of $26$ tons, what

power is required to drive each screw when the gate is being raised at the rate of $3f\frac{t}{m}in?$

What is the corresponding rotating speed of the screws?