Question

16. A loaded elevator is raised by a motor that is rated at 3.65 x 104W. The motor raises the elevator at a steady speed of 3.10 m/s up. What is the mass of the elevator and its occupants?

Answer 1

GIVEN: The power rating of an elevator,

Speed of the elevator, v = 3.10 m/sec (upward)

Solution: Let the total mass of the elevator and its occupants be 'M'

When an object having mass lies or stand on a surface, a normal force acts on it towards the centre of mass of the object/ system and perpendicular to the surface.

Thus, the net force is given by,

  

here, N - normal force,

Mg - the weight of the object,

a - the net acceleration of the system

  

In the given problem, since the elevator is moving steadily, thus, its net acceleration will be equal to zero.

i.e., N - Mg = 0

==> N = Mg

Since, the loaded elevator is rated at the power given which is required to raise the load which has normal reaction equal to N, thus, to calculate the total mass, we know that

P = N. v

Here, P - power rated,

N - normal force,

v - speed

Therefore,