Homework question using the chain rule -- oil slick spreading on the sea....

[Dousin12]

<Moderator's note: Moved from a technical forum and thus no template.>

Question: A certain amount of oil on the sea surface can be considered as circular form
and the same thickness throughout its surface. At a certain time, the following are noted
Data: Oil is supplied to the spot at 5m^3/min , the radius is 50 m, the thickness
0.003m and the radius increases (at this time) at 4m/ min.Does the thickness of increase or decrease at the stain at the current time? With what speed does this happen?

My thoughts:
dV/dt=dV/dr * dr/dt , where dr/dt is given and dV/dt is given. However dV/dr I am unsure, coz maybe u should do dV/dh? However. If u use dV/dr, i get that that is equal to (pi*r^2*h)'=2*pi*r*h , and given the data for r, u solve the equation for h? The h i get i take minus the h i had before and that must be the change, however, I get the wrong answer. Where is my thought process wrong?

 

[Mark44]

<Moderator's note: Moved from a technical forum and thus no template.>

Question: A certain amount of oil on the sea surface can be considered as circular form
and the same thickness throughout its surface. At a certain time, the following are noted
Data: Oil is supplied to the spot at 5m^3/min , the radius is 50 m, the thickness
0.003m and the radius increases (at this time) at 4m/ min.Does the thickness of increase or decrease at the stain at the current time? With what speed does this happen?

My thoughts:
dV/dt=dV/dr * dr/dt , where dr/dt is given and dV/dt is given. However dV/dr I am unsure, coz maybe u should do dV/dh? However. If u use dV/dr, i get that that is equal to (pi*r^2*h)'=2*pi*r*h , and given the data for r, u solve the equation for h? The h i get i take minus the h i had before and that must be the change, however, I get the wrong answer. Where is my thought process wrong?

You are given that the slick is uniform in thickness, so you are given h.

Also, do not use textspeak such as "coz" and "u" in place of "because" and "you." From the forum rules:

SMS messaging shorthand ("text-message-speak"), such as using "u" for "you", "please" for "please", or "wanna" for "want to" is not acceptable.

 

[Nidum]

I don't think we are supposed to interpret that thickness as constant . The incoming oil is causing the slick to spread at the given rate . The thickness may be getting larger or smaller with time depending on the numbers .

 

[Mark44]

I don't think we are supposed to interpret that thickness as constant . The incoming oil is causing the slick to spread at the given rate . The thickness may be getting larger or smaller depending on the numbers .

From the problem statement:

A certain amount of oil on the sea surface can be considered as circular form
and the same thickness throughout its surface.

 

[Nidum]

The same thickness throughout it's surface yes but the actual value of that thickness is changing with time .

 

[Mark44]

The same thickness throughout it's surface yes but the actual value of that thickness is changing with time .

That might make for a more realistic problem, but I doubt very much that this is the assumption for this problem.

 

[Ray Vickson]

That might make for a more realistic problem, but I doubt very much that this is the assumption for this problem.

The problem asked "Does the thickness of increase or decrease at the stain at the current time? With what speed does this happen?" I'm not sure what the "at the stain" phrase refers to, but I would assume that somehow the spill magically spreads out instantly to a larger radius at a (possibly new) thickness.

 

[Mark44]

My apologies @Nidum and Ray - I read the problem statement too quickly and misinterpreted what it was saying.

Ray, I believe "at the stain" refers to the entire oil stain. The sentence you quoted is somewhat garbled. I think this is what the author intended:
"Does the thickness of the oil stain increase or decrease at the stain at the current time?"

 

[Ray Vickson]

My apologies @Nidum and Ray - I read the problem statement too quickly and misinterpreted what it was saying.

Ray, I believe "at the stain" refers to the entire oil stain. The sentence you quoted is somewhat garbled. I think this is what the author intended:
"Does the thickness of the oil stain increase or decrease at the stain at the current time?"

Yes, that is in line with what I said, more-or-less, in the last part of my second sentence.