Question

Two electric motors drive two elevators of equal mass in a three-story building 10 meters tall. Each elevator has a mass of 1,000 kg. The first elevator can do this work in 5.0 seconds. Calculate the power output of the first motor.

2.0 x 102 W
2.0 x 103 W
2.0 x 104 W
2.0 x 105 W

Answer 1

Power output =
`2* 10^4\ W`

Step-by-step explanation:

Given:

Mass of the elevator is,
`m=1000\ kg`

Height to which it is raised is,
`h=10\ m`

Acceleration due to gravity is,
`g=10\ m/s^2(Approximately)`

Time taken by the motor to raise the elevator is,
`t=5.0\ s`

Now, work done on the elevator by the motor is equal to the increase in the gravitational potential energy of the elevator.

Increase in gravitational potential energy is given as:

`\Delta U=mgh=(1000)(10)(10)=10* 10^4\ J`

Therefore, work done by motor is,
`W=10* 10^4\ J`

Now, we know that, power is work done in unit time. So, power output is given as:

`Power=(W)/(t)\\\\Power=(10* 10^4\ J)/(5.0\ s)\\\\Power=2* 10^4\ J/s\\\\Power=2* 10^4\ W..........[1 W = 1\ J/s]`

Therefore, the power output of the first motor is
`2* 10^4\ W`