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Solve Exercise 24 if the tank is half full of oil that has a density of $ 900 kg/m^3 $.
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Calculus 2 / BC
Chapter 6
Applications of Integration
Section 4
Work
Missouri State University
University of Michigan - Ann Arbor
Boston College
Lectures
01:06
Solve Exercise 20 if the t…
05:32
tank is is half full of ol…
08:36
A tank is is half full of …
03:24
(a) The tank shown is full…
01:04
Solve Exercise 8 assuming …
02:02
In Fig. P2.12 the tank con…
01:03
Determine the volume (in $…
02:55
Think About It Approximate…
So we first need to figure out the geometry of the setting. Here we have a sphere which is a sphere to tank and there's a little pipe. The radius of this sphere 3, and this little pipe has length 1 point. Okay, so think of the object is right there and but the pythagorean theorem. We have the distance of the coordinates of this. If this little object is x and y, and here 3, so we have x, squared plus y square, equals 9 by the pythagorean and x equals to 9 minus y squared so calculate the total work. We'Re going to fly the formula that the work equals to f d s from a to b, starting in position and f here, equal to p v times. G were pasdensity base. Volume and g is the gravity the force of the gravity, which is to 9.8 point. So we have that in this formula is goes to a from a to b, p b g times the distance called l b. S in this problem were given that t is 900, i joves 9.8 and the distance that the object is to travel. Is the total length is r plus l so which is 4 minus y y? The vertical the vertical the vertical coordinates of the object and the x is horizontal, coordinates so the distance here we could carol to distinguish the length of the pipe, so is feminus y and what is the volume? The voltumn here is simply high r squared, but r. Here is not a radius of the ball of the square; it is the radius of the slice of a circle where the object is located in. It is only an uncertain circle, so the radius here just the x, coordinate the object so which is equal to pi times 9 minus e square, so hans integral goes to 0 and negative 3 start from both square 900 times 9.8 times 4 minus y times 9. Minus y, squared and pi so integral is the y evaluating this integral can give us a roughly 8.13 pi times 10 to the 5. That'S the total work. You'Re gonna do.
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