Question

A person with mass m= 70 kg takes the elevator to the top of the Empire State Building at a height of 300 m. Assum the elevator takes 1 min to reach the top of the building

(a) Find the work done on the person by gravity during the elevator ride?

(b) Find the amount of work the normal force of the floor did on the person.

(c) Find the average power of the force of gravity.

Answer 1

Given is:-

mass of the person m=70 kg

height of the building h=300 m

time takne by the elevator t= 1 minute = 60 seconds

now,

part-a

Force due to the gravity on to the person is

Work done is given by

negative sign shows that the force is in opposite direction to the displacement

the net work done by the gravity is

Part-b

According to the Newton's second law

or

eq-1

Using second equation of motion we get

by plugging all the values we get

whcih gives us

by plugging all the values in eq-1 we get

which gives us

hence the work done by the normal force on to the person is

But if the elevator is not accelerating or it moves with constant speed then

Part-c

The average power of the force of gravity is

which gives us