Question

An escalator with 35° incline is designed to have two passengers per step. Find number of persons moved per hour for the design if velocity is 50cm/mins and the step tread is 600mm.

Answer 1

Answer:

The escalator disposes 58 passengers each hour.

Explanation:

The velocity diagram of the escalator is shown in the attached figure

We can obtain the vertical distance that the escalator moves in 1 hour as

$D_{v}=vsin(\theta )\times 1hr\\\\D_{v}=50cm/min\times sin(35^{o})\times 60mins\\\\\therefore D_{v}=1720.73cm$

Thus in 1 hour the last thread moves 1720.73 cm

Now it is given that 1 thread = 600 mm =60 cm

Thus the number of times the last thread moves equals

$n=\frac{1720.73}{60}=28.68times$

Since each time last thread moves it disposes 2 passengers thus the number of passengers disposed when the thread moves 28.68 times equals

$N=28.68\times 2=57.36$

Thus the escalator disposes 58 passengers each hour.