Find the work done in pumping gasoline that weighs 40 pounds per cubic foot. ( H

Question

Find the work done in pumping gasoline that weighs 40 pounds per cubic foot. (Hint: Evaluate one integral by a geometric formula and the other by observing that the integrand is an odd function.)

A cylindrical gasoline tank 3 feet in diameter and 4 feet long is carried on the back of a truck and is used to fuel tractors. The axis of the tank is horizontal. The opening on the tractor tank is 5 feet above the top of the tank in the truck. Find the work done in pumping the entire contents of the fuel tank into the tractor. (Round your answer to three decimal places.)

____ft-lb

Explanation / Answer

The work done to move an extended object is to calculate the change in Potential Energy(PE) of its center of mass.
Gas has a weight of;

Mg = (pi)r^2 Length* Density = (pi)(1.5)^2(4)*(40) = 360 lbs

The Center of mass is to be lifted height (h) = 1.5 + 5 = 6.5 ft    (radius = diameter/2 = 3/3 =1.5)

Change in PE = ( Mg) *(h )= (360)(6.5) = 2340ft-lbs -------------ans.

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