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 constance 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 80 s?
B. What is the power delivered by the escalator in watts?
C. What is the maximum mass of people can the escalator deliver in 80 s while working at its maximum power capacity?
Aaanz s
To answer these questions, we need to use the formula for work and power. Work is defined as the product of force and displacement, and power is defined as the rate at which work is done.
A. To find the work done in 80 s, we need to multiply the force by the displacement. We know that the force (F) is equal to the weight of the people being lifted, which can be calculated as the mass (m) multiplied by the acceleration due to gravity (g).
First, let's find the force:
F = m * g
F = 18 * 73 * 9.8 (mass * average mass * acceleration due to gravity)
F ≈ 12,856 N
Now, we can calculate the work done by multiplying the force by the vertical displacement (d) of 6.8 m:
Work = force * displacement
Work ≈ 12,856 N * 6.8 m
Work ≈ 87,660 J
Therefore, the work done in 80 s is approximately 87,660 Joules.
B. Power is the rate at which work is done. It can be calculated by dividing the work done by the time it takes to do that work. In this case, we need to convert the time given in seconds to minutes.
Power = Work / Time
Power = 87,660 J / 80 s ≈ 1096.25 W
Therefore, the power delivered by the escalator is approximately 1096.25 Watts.
C. To find the maximum mass of people the escalator can deliver while working at its maximum power capacity, we need to rearrange the power formula and solve for mass.
Power = Force * Velocity
Force = Power / Velocity
We know that the velocity is constant, so we can substitute the given power consumption of 0.22 of its maximum power capacity to find the force:
Force = 0.22 * Maximum Power Capacity
Then, we can calculate the maximum mass by dividing the force by the acceleration due to gravity:
Maximum Mass = Force / (average mass * g)
Let's assume the maximum power capacity is P:
Force = 0.22 * P
Maximum Mass = Force / (average mass * g)
Maximum Mass = (0.22 * P) / (73 * 9.8)
We can use these formulas to solve for the maximum mass given the maximum power capacity of the escalator.