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

`\eta = 70.711\,\%`

Step-by-step 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\,(persons)/(min)\right)\cdot (124\,lbm)\cdot \left(32.174\,(ft)/(s^(2))\right)\cdot \left((1\,lbf)/(32.174\,(lbm\cdot ft)/(s^(2)) ) \right)\cdot (27.5\,ft)`

`\dot W = 88660\,(lbf\cdot ft)/(min)\,\left(2.687\,hp\right)`

The mechanical efficiency of the escalator is:

`\eta = (2.687\,hp)/(3.8\,hp)* 100\,\%`

`\eta = 70.711\,\%`