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

The escalator disposes 58 passengers each hour.

Step-by-step 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 )* 1hr\\\\D_(v)=50cm/min* sin(35^(o))* 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=(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* 2=57.36`

Thus the escalator disposes 58 passengers each hour.