Intergration to find work is from 0 to Y

In summary, the question is about the total work required to plumb oil or water from a circular cylinder buried under the Earth's surface to the surface. For a vertically standing cylinder with depth Y of oil or water, the integration for work is from 0 to Y. For a horizontally standing cylinder, the integration is from the top of the cylinder to the surface, which would be the diameter to diameter+X. However, if there is no oil in the cylinder, there is no work to be done.
  • #1
d_b
36
0
I have a question. If i have an object let say a circular cylinder buried underneath the Earth surface with X as its depth. I'm looking for the total work to plumb the oil or water that is in the cylinder to the surface

if the cylinder stand virtically and has water or oil in it(Y as its depth of water or oil) then the intergration to find work is from 0 to Y. Right??

and if the cylinder stand horizontally still with oild or water in it then the intergration is from the top part of th cylinder (the diameter)to the surface(diameter+ X), right??

and what if their is no oil in the cylinder? what would the intergration be?
 
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  • #2
d_b said:
I have a question. If i have an object let say a circular cylinder buried underneath the Earth surface with X as its depth. I'm looking for the total work to plumb the oil or water that is in the cylinder to the surface
…
and what if their is no oil in the cylinder? what would the intergration be?

Hi d_b! :smile:

I don't follow … if there's no oil, what are you plumbing? :confused:
 
  • #3


hm...good question. i totally didn't see that. Anyhow still if i was to left an object up then the work that is going to be done on it is up to the depth of the oil?

i read i few other site and it seems that every work that is done on the object is up to the line where the water or oil is (the intergration)but I'm just not sure how to picture that if the object is under the surface or some sort.
 

1. How is integration used to find work from 0 to Y?

Integration is a mathematical tool used to find the area under a curve. In this case, the curve represents a function that represents the relationship between the independent variable (x) and the dependent variable (Y). When integrating from 0 to Y, it means finding the area under the curve between the values of 0 and Y on the x-axis.

2. Why is integration used to find work?

Integration is used to find work because it allows us to calculate the total amount of work done by a variable force, which can be represented by a curve on a graph. By finding the area under the curve, we can determine the total work done over a specific distance or time interval.

3. Can integration be used to find work for any type of variable force?

Yes, integration can be used to find work for any type of variable force, as long as the force can be represented by a continuous function. This includes both simple and complex forces, such as linear, quadratic, and trigonometric functions.

4. How does the value of the integral relate to the amount of work done?

The value of the integral represents the area under the curve, which is directly proportional to the amount of work done. This means that the larger the area under the curve, the greater the amount of work done.

5. Are there any limitations to using integration to find work?

One limitation of using integration to find work is that it assumes a constant force is applied over small intervals, which may not always be the case in real-world scenarios. Additionally, integration may not be applicable for calculating work done by non-conservative forces, such as friction or air resistance.

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