Question

An experimental electrical generator collects sunlight with mirrors and generates heat at a rate of 1.2 megawatts. The generator is mounted on the roof of an environmentally friendly building and is used to operate an elevator. The elevator has a maximum operating load of 8000 kg and a maximum velocity of 6 m/s.

A. Determine the power that the generator must supply to operate the elevator at its maximum operating

B. What is the efficiency of this system?

Answer 1

Answer:

a) 0.47MW

b) 39.24%

Explanation:

In order to find the power needed for the elevator to operate at its maximum capacity, we can make use of the following formula:

P=Fv

where P is the power, F is the force and v is the velocity.

The force the elevator must carry can be calculated with the following formula:

F=mg

where m is the mass of the elevator and g is the acceleration of gravity, so:

$F=(8000 kg)(9.81 m/s^{2})$

F=78 480 N

so now we can make use of the power formula:

P=Fv

P=(78 480N)(6 m/s)

P=470 880W

P=0.47W

b)

In order to find the efficiency, we will suppose that the generator can generate a maximum of 0.47 W so we use the following formula:

$efficiency = \frac{P_{in}}{P_{out}}*100\%$

$efficiency=\frac{0.470880}{1.2}*100\%$

efficiency=39.24%