Question

An escalator in a shopping center is designed to move 50 people, 75 kg each, at a constant speed of 0.6 m/s at 45° slope. Determine the minimum power input needed to drive this escalator

Answer 1

Answer:

$\dot E = 15602.842\,W$

Explanation:

By an adequate application of the Principle of Energy Conservation, the escalator need energy to elevate from to the bottom to the top. Hence:

$E = m_{total}\cdot g \cdot y$

An expression for power needed is found by deriving the equation with respect to time:

$\dot E = m_{total}\cdot g \cdot v_{y}$

The minimum power is found by substituting known inputs:

$\dot E = (50)\cdot (75\,kg) \cdot (9.807\,\frac{m}{s^{2}} )\cdot (0.6\,\frac{m}{s} )\cdot \sin 45^{\textdegree}$

$\dot E = 15602.842\,W$