(a) How much work does an elevator motor do to lift a 1000 kg elevator a height of 100 m? (b) How much power must the motor supply to do this in 50 s at constant speed?

Video transcript

Hey, everyone. So this problem is a pretty straightforward power question. Let's see what they're asking us. We need to determine the power a crane engine requires to raise a 4500 kg container by 4. m in 15 seconds at a constant speed. Our multiple choice answers here are a 1.2, 6 kW. B 158 kW C 12. kW or D 16.1 kW. So the first thing we're going to do for this problem is recall that power is given to us as work over delta time, delta T for time, our work in turn, we can recall is our force times the distance or the displacement of the particle of the force is acting from there. We can draw our free body diagram of this container. So as the crane is raising the container, we have an upward force from the crane. So we'll call that sub C and then we have the weight of the container acting in a downward direction from Newton's second law. We can recall that the sum of the forces is equal to mass times acceleration because we're told that we are at a constant speed, our acceleration is going to be zero. So that whole term goes to zero. So the sum of our forces here are going to be F C minus weight equals zero or F C is equal to. So wait from there, we can recall that weight it's given to us as mass times gravity And the mass and the problem was given as 4500 kg. We can recall that gravity is a constant 9.8 m per second squared, which gives us force of the crane Of 4.4, 1 times 10 to the four s substituting this W equation into our power equation. We have power equals force of the crane times the displacement over delta T you solve for force of the crane. That's 4.41 10 10 to the fourth newtons or displacement is 4. m is given in the problem And our delta TR change in time is 15 seconds. We can plug that into our calculators and we are left with 12. kW. So that is the answer to this problem. And that aligns with answer choice C. That's all we have for this one. We'll see you in the next video.