Basic Physics (Work, Power and Energy - Law of Conservation)

Question

Good day to everyone, I would like to request a help from this one. Please do provide a detailed step-by-step, explanation and a clear final answer.

1. A passenger in the airport pushes a 53-kg suitcase at an inclined floor of 25° of 12.5 meters using a horizontal force of 40 N at a constant speed of 0.5 𝑚⁄𝑠 . How much work does the passenger does throughout the motion? Assume that it is a non-fiction floor.
2. An elevator is transporting 14 persons every minute from the first floor of a school building to the second. The second floor is located 3.5 meters above the first floor. The average mass of a person in the elevator is 45 kg, determine the power requirement of the escalator to move this number of passengers in one minute.

Thank you very much! Please explain as detailed as possible towards the step-by-step procedure with explanation with each steps and a final answer with explanation too. God bless and keep safe!

Answer 1

Let me first do problem 2. and then come back to problem 1.

Let

n = 14 be the number of people,

h = 3.5 m be the distance travelled,

m = 45 kg be the mass per person,

t = 1 min = 60 sec be the time it takes,

g = 9.81 m/s² be gravitational acceleration.

Notice that the first step above is to convert everything to standard units:

kg, m, s.

I assume no friction or any other kind of resistance.

The problem does not mention the mass of the elevator,

so I will assume it to be 0. So the total mass

M = n×m

In general, power

P = W/t

where W is the work performed by the elevator.

In this case it is easiest to calculate the work W from the equivalence

between work and gain in energy.

There are two kinds of mechanical energy -- kinetic and potential.

There is no change in kinetic energy if we assume that the elevator starts

from rest and then stops at the destination.

There is a gain in potential energy due to the gain in height.

The gain in potential energy, and hence the work W, is

W = Mgh

(If you do not know how to calculate potential energy, let me know.)

Thus the power is

P = Mgh/t

Substituting actual numbers

P = 14×45×9.81×3.5/60 = 360.5 W

Problem 1.

You write "Assume that it is a non-fiction floor."

I assume "Assume that it is a non-friction floor.

In that case the situation described is impossible on planet Earth.

The only way the force of 40 N exerted by the passenger would not cause

any acceleration, is if it is exactly balanced with the force of gravity

pulling the suitcase back.

Assuming that the situation is on Earth, the force of the passenger

is much too small to prevent the suitcase from sliding back.

So some of the given data has to be ignored.

I will ignore the force of 40 N, because judging from problem 2. you are expected to use

the equivalence between work and energy gain, in which case the force is irrelevant.

I will also ignore the speed of 0.5 m/s.

The amount of work NEVER depends on the speed or even on the trajectory taken.

The only relevant information is the initial and final position and the

initial and final speed. In this case knowing that the initial and final speeds

are the same is sufficient.

Let

M = 53 kg be the mass of the suitcase,

s = 12.5 m be the distance pushed,

α = 25° be the angle,

h = s×sin(α) be the height gained,

g = 9.81 m/s² be gravitational acceleration.

So we will calculate the work from the gain in potential energy, just like

in problem 2.

W = Mgh

Substituting actual numbers

W = 53×9.81×12.5×sin(25°) = 2747 J