Question

The loaded cab of an elevator has a mass of 3.0⇥ 103 kg and moves 210 meters up the elevator shaft in 23 seconds at constant speed. At what average rate does the force from the cable do work on the cab? (Hint: Power. The work from the cable must overcome the force of gravity.)

Answer 1

Answer:

$P=268kW$

Explanation:

Given data

Mass of elevator m=3.0×10³kg

Time t=23 seconds

Height d=210 m

Concept:

Power is defined as rate at which work is done by force is said to be the power due to force.

The power can be calculated as

$P=FVCos\alpha$

First we need to find the force by applying newtons law of motion

So

$F=mg\\F=(3000kg)(9.8m/s^2)\\F=29400N$

Now we need to find the velocity V

So

$V=distance/time\\V=210m/23s\\V=9.13m/s$

Now to put values of Force and velocity to find the power.As the force have same direction of motion so angle is zero

$P=FVCos\alpha \\P=(29400N)(9.13m/s)Cos(0)\\P=268kW$