A(n) 712 kg elevator starts from rest. It moves upward for 3.13 s with a constant acceleration until it reaches its cruising speed of 1.93 m/s. The acceleration of gravity is 9.8 m/s 2 . Find the average power delivered by the elevator motor during this period. Answer in units of kW.

P = 7.61kW

Explanation:

In order to calculate the power delivered by the elevator motor, you take into account the work done by the elevator against the gravitational force.

The work done by the elevator is given by:

    (1)

F: force of the motor

M: mass of the elevator = 712 kg

g: gravitational force = 9.8 m/s^2

h: vertical distance traveled by the elevator

a: acceleration of the elevator

You calculate the acceleration a by using the following formula:

      (2)

With this values you can calculate F from (1)

    (3)

Furthermore, you have that the work is equal to the change in the kinetic energy:

    (2)

v: final speed of the elevator = 1.93 m/s

vo: initial velocity = 0 m/s

From the equation (2) you can calculate the vertical distance h:

Then, the work done by the elevator is

The quotient of the work We and time (3.13 s) is the power delivered by the motor:

The power delivered by the elevator is 7.61kW

so here is the information for current research:

-nrel's geothermal analysts, scientists, and engineers perform a full range of research from developing advanced methods of locating and accessing geothermal resources to exploring innovative technologies to extract and produce clean energy from the heat of the earth

and here is the information for the technology of geothermal energy:

-it's clean and sustainable

-resources of geothermal energy range from the shallow ground to hot water and hot rock found a few miles beneath the earth's surface, and down even deeper to the extremely high temperatures of molten rock called magma

-almost everywhere, the shallow ground or upper 10 feet of the earth's surface maintains a nearly constant temperature between 50° and 60°f (10° and 16°c)

-geothermal heat pumps can tap into this resource to heat and cool buildings

-a geothermal heat pump system consists of a heat pump, an air delivery system (ductwork), and a heat exchanger-a system of pipes buried in the shallow ground near the building

-in the winter, the heat pump removes heat from the heat exchanger and pumps it into the indoor air delivery system

-in the summer, the process is reversed, and the heat pump moves heat from the indoor air into the heat exchanger

-the heat removed from the indoor air during the summer can also be used to provide a free source of hot water