Work compute with integral
A tank is full of water. Find the work W required to pump the water out of the spout. Use the fact that water weighs 62.5 lb/ft3.
a = 5 b = 9 c = 12
So for this one, you have to set up an amount of rectangles.
The biggest rectangle is 5(or y) by 9, in relation to a smaller rectangle that is w by 9. I can also setup a relationship between the two to find that y/w=9/9 or y=w. So therefore we can produce an equation for the area of one rectangle.
Now the thickness of this rectangle is extremely small so the thickness is dy.
The density of water is 62.5 lb/ft^3, so this one rectangular-box of water is:
To find the force, we multiply by the force of gravity, I used 32.2 ft/sec^2.
So our work is dF times the distance. This is where I become lost. Would the distance be vertical or horizontal? would it be (5-y) or (12-y)?