An escalator in a department store is driven by a large electric motor whose power consumption changes with the load to keep the escalator moving at a constant velocity, up to a certain maximum power capacity. an escalator working at 0.22 of its maximum power capacity lifts 18 people per minute a vertical height of 6.8m. these people have an average mass of 73kg.
a) how much work is done in 80s?
b) what is the power delivered by the escalator in watts?
c) what is the maximum mass of people can the escalator deliver in 80s while working at its maximum power capacity.
To solve these questions, we need to understand the concepts of work, power, and how they relate to each other.
a) To find the work done in 80 seconds, we can use the formula:
Work = Force × Distance
First, let's find the force exerted to lift one person. The force is equal to the person's mass multiplied by the acceleration due to gravity (9.8 m/s^2):
Force = mass × acceleration due to gravity
Force = 73 kg × 9.8 m/s^2
Force = 715.4 N
Next, we calculate the total force required to lift 18 people simultaneously:
Total Force = Force per person × Number of people
Total Force = 715.4 N × 18
Total Force = 12,877.2 N
Now, we can calculate the work done by the escalator in lifting this total force over a vertical distance of 6.8 m:
Work = Force × Distance
Work = 12,877.2 N × 6.8 m
Work = 87,593.76 Joules
Therefore, the work done in 80 seconds is 87,593.76 Joules.
b) Power is the rate at which work is done, and it can be calculated using the formula:
Power = Work / Time
Let's calculate the power delivered by the escalator in watts:
Power = Work / Time
Power = 87,593.76 J / 80 s
Power = 1,094.92 watts
Therefore, the power delivered by the escalator is 1,094.92 watts.
c) The maximum power capacity mentioned is not given in the question. We only know that the escalator is working at 0.22 of its maximum power capacity while lifting 18 people per minute.
In order to find the maximum mass of people the escalator can deliver in 80 seconds while working at its maximum power capacity, we need additional information such as the maximum power capacity of the escalator. Without this information, it is not possible to answer this question.
mass = m = 18 * 73 = 1314 kg of people (not too very fat ones)
h = 6.8 meters
work done = force * distance = m g h = 1314 * 9.81 * 6.8 = 87,654 Joules
This was evidently done in 80 seconds That is not explicitly stated)
power out = work done in Joules / time in seconds = 87654/80
= 1,096 Watts
at maximum capacity, same height, same speed, same earth gravity so
1314/0.22 = 5973 kg