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Homework Statement
A small motor is used to operate a lift that raises a load of bricks weighing 500N to a height of 10m in 40s at constant speed. The lift weighs 300N. What is the work done by the force of the motor? What is the work done by the force of gravity?
Homework Equations
[itex]P = \vec{F} \cdot \vec{v}[/itex]
[itex]W = \vec{F} \cdot \vec{l}[/itex]
The Attempt at a Solution
Since power is work done over a time interval (J/s), I figured that if I found the total power, I could multiply that by the time taken to get the total work done:
[itex]P = \vec{F} \cdot \vec{v}
= Fv*cos(\phi)[/itex]
The angle is 0 since the bricks are being lifted straight up, so that simplifies to P = Fv.
Force is the sum of the weight of the bricks and the lift (500N + 300N = 800N)
Found the average velocity:
v = (10m) / (40s) = 0.25m/s
This gives me an average power output of (800N * 0.25m/s) = 200W. Multiply this by 40 seconds, and I get the total work done, which is 8000 J.
Now I'm stuck. At first I thought that I could then calculate the work done by gravity and then subtract it from total work done to get the work done by the motor, but I'm not sure how to go about doing this or if that's even the right way to go about it.