Question

An escalator handles a steady load of 26 people per minute in elevating them from the first to the second floor through a vertical rise of 27.5 ft. The average person weighs 124 lb. If the motor which drives the unit delivers 3.8 hp, calculate the mechanical efficiency e of the system.

Answer 1

Answer:

$\eta = 70.711\,\%$

Explanation:

The power needed to make the escalator working is obtained by means of the Work-Energy Theorem:

$\dot W = \dot U_{g}$

$\dot W = \dot n \cdot m_{p}\cdot g \cdot \Delta y$

$\dot W = \left(26\,\frac{persons}{min}\right)\cdot (124\,lbm)\cdot \left(32.174\,\frac{ft}{s^{2}}\right)\cdot \left(\frac{1\,lbf}{32.174\,\frac{lbm\cdot ft}{s^{2}} } \right)\cdot (27.5\,ft)$

$\dot W = 88660\,\frac{lbf\cdot ft}{min}\,\left(2.687\,hp\right)$

The mechanical efficiency of the escalator is:

$\eta = \frac{2.687\,hp}{3.8\,hp}\times 100\,\%$

$\eta = 70.711\,\%$