So here is the question: A rectangular tank with base 4 feet by 5 feet and a height of 4 feet is full of water. The water weighs 62.4 pounds per cubic foot. How much work is done in pumping the water out over the top edge in order to empty A) half of the tank. B) all of the tank.
So what I did was the following; Since the weight equal force F we have F = 62.4-lbs And the volume of a rectangle is l.b.h, so that is 4.5.4 = 80 ft^3 Then I just plug in using integrals.
A) w = 80 from 0 to 1/2 of 62.4 dx and that is equal to 62.4x and then I substitute and I got 2496 ft-lbs Which is the correct answer according to my book.
B)
w = 80 from 0 to 2 of 62.4 dx and that is equal to 62.4x and then I substitute and I got 9984 ft-lb which is correct. Now my question is, is the process of doing this correct?. I used common sense to set up the limit of integration.