Question

There is a cylindrical barrel with radius 1 and height 4. It is half full of oil and the oil weights 50lb/ft^3. If we want to pump the oil from the bottom to the top of the barrel, how much work is done?

I made the distance from the top of the barrel to a certain point of the barrel "x" so that the volume of the oil being pumped up is " pi(1)^2*x " and the weight would be 50 times this. The distance that this guy has to travel is "4-x". The limits of the integration I chose was from 2 to 4. I calculated the answer to be 400pi/3 but the actual answer is 300pi.

Can someone help me ?

Answer 1

work = force times distance

Answer 2

let me see if I recall the formula..

Answer 3

distance moved is from 4-y for any given section;

weight for any given volume is 50 times pir^2

Answer 4

yep

Answer 5

since it is half full we integrate from 0 to 2

Answer 6

[S] 50pi r^2 (4-y) dy sound about right?

Answer 7

The answer was right, but one question.

Answer 8

yes?....

Answer 9

Is the volume of the cylindrical oil considered as 50(pi)r^2 dx ?

Answer 10

r in this case is a constant i beleive since the shape has straight sides

Answer 11

if it was conic; then radius would change with respect to x or y depending on its orientation

Answer 12

sin ce we are lifting in the vertical direction; the sums are added vertically up the y..or down the y :)

Answer 13

Let me try it again and see if I can do it on my own.

Answer 14

ok :) I think you can ;)

Answer 15

Great, it was a simple mistake I had there. I get it now. I really appreciate your help. I have to take a AP calculus diagnostic exam next week for a job interview and it will decide if I can marry my girl or not.