Calculus 2 Applications to physics Cylindrical Problem
A vertical right circular cylindrical tank measures 24 ft high and 12 ft in diameter. It is full of oil weighing 60lb/ft3. How much does it take to pump the oil to a level 2 ft above the top of the tank? Give your answer to the nearest ft lb.
A vertical right circular cylindrical tank measures 24 ft high and 12 ft in diameter. It is full of oil weighing 60lb/ft3. How much does it take to pump the oil to a level 2 ft above the top of the tank? Give your answer to the nearest ft lb.
So work is equal to Force times Distance
First we need to find the volume of a little slice(they are little cylinders)
this is in cubic feet. To convert this to a force use the above to get
We know that we have to move each slice x+2 feet so ...
Makes sense, so to finish the problem you will just integrate and plug in 24 and 2? and would it be from 24 to 2 because it wants it to be " 2ft above the tank?"
Makes sense, so to finish the problem you will just integrate and plug in 24 and 2? and would it be from 24 to 2 because it wants it to be " 2ft above the tank?"
Not quite the x+2 is the distance moved so we only need to integrate from 0 to 24.
for instance the slice on top at x=0 only moves 0+2ft=2ft