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

Answer:

Power output = $2\times 10^4\ W$

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:

$\Delta U=mgh=(1000)(10)(10)=10\times 10^4\ J$

Therefore, work done by motor is, $W=10\times 10^4\ J$

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

$Power=\frac{W}{t}\\\\Power=\frac{10\times 10^4\ J}{5.0\ s}\\\\Power=2\times 10^4\ J/s\\\\Power=2\times 10^4\ W..........[1 W = 1\ J/s]$

Therefore, the power output of the first motor is $2\times 10^4\ W$