Answer:
[tex]\eta = 70.711\,\%[/tex]
Explanation:
The power needed to make the escalator working is obtained by means of the Work-Energy Theorem:
[tex]\dot W = \dot U_{g}[/tex]
[tex]\dot W = \dot n \cdot m_{p}\cdot g \cdot \Delta y[/tex]
[tex]\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)[/tex]
[tex]\dot W = 88660\,\frac{lbf\cdot ft}{min}\,\left(2.687\,hp\right)[/tex]
The mechanical efficiency of the escalator is:
[tex]\eta = \frac{2.687\,hp}{3.8\,hp}\times 100\,\%[/tex]
[tex]\eta = 70.711\,\%[/tex]
