Question
A spherical tank of radius 100ft is full of gasoline weighing 40 pounds per cubic feet how much work is done in pumping the gasoline to the top of the tank?
Answers
oobleck
why bother? The tank is already full.
But, let's say that you want to pump all the gas up to the top of the tank
total weight: 4/3 π r^3 * density = 167,551,608.91 lbs
moving the center of mass up 100 ft will take 16,755,160,891 ft-lbs of work
You can use calculus and integrate, moving the weight of all the thin slices of gasoline their respective distances, but it will come out the same.
But, let's say that you want to pump all the gas up to the top of the tank
total weight: 4/3 π r^3 * density = 167,551,608.91 lbs
moving the center of mass up 100 ft will take 16,755,160,891 ft-lbs of work
You can use calculus and integrate, moving the weight of all the thin slices of gasoline their respective distances, but it will come out the same.