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aktanuku

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## Homework Statement

Consider placing a short length of small diameter steel (specific weight =490 lb/ft^3) rod on the surface of water. What is the maximum diameter that the rod can have before it will sink? Assume the surface tension forces act vertically upward.

## Homework Equations

volume of cylinder = pi*r^2h

## The Attempt at a Solution

I don't know if this is correct.

I am assuming the rod is lying flat on the water not standing up (like this: _ ; not like this: |) also i am assuming that the rod is half way submerged so surface tension forces are acting on on exactly half of the surface area of the rod. So the surface area of a cylinder (excluding the top and bottom) is given by 2*pi*r*h. Since i want half of that i should get pi*r*h. assume a coefficient of surface tension sigma. surface tension=sigma*pi*r*h

Since the rod has a specific weight of 490 lb/ft^3 we can multiply this by the volume of a cylinder (pi*r^2*h) and get the downward force.

Since the rod is floating these forces must be in equilibrium. Thus,

pi*r^2*h*490 = sigma*pi*r*h

so r= sigma/490

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