In exercise 23, find the work done in pumping gasoline that weighs 42 pounds per

Question

In exercise 23, find the work done in pumping gasoline that weighs 42 pounds per cubic foot. (Hint: Evaluate one integral by a geometric formula and the other by observing that the integrand is an odd function).

23) 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 thank 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.

Explanation / Answer

the easiest way to find the work done to move the fuel into tractor is to calculate the change in potential energy of its centre of mass.

the gas has a weight of mg=(pi)r2LD

here r will be d/2 = 3/2 = 1.5,l is 4 and D is 42lb

so mg = (pi)(1.5)2(4)(42) = 378(pi) lbs

the centre of mass is lifted by h = 1.5+5 = 6.5

so change is PE is MGH=(378(pi))(6.5)=2457(pi)ft-lbs.

so work done is 2457(pi) ft-lbs

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