Steel ball floating due to surface tension?

[magnusbarclay]

Hey!

Been doi some coursework from a text but can't seem to find any solutions so don't know if I am even remotely close to the right answer.

Q. A steel ball can float on water due to the surface tension effect.

a) Determine the maximum diameter of a steel ball that would float on water at 20 degrees.

b) What would be the maximum diameter for an aluminium ball.

Assume the densities of steel and aluminium to be 7800 kg/m^3 amd 2700 kg/m^3 respectively

I would appreciate working if possible. Thanks

 

[cipher42]

Could you use the standard template for homework help problems and give us what you think are the relevant equations and your attempt at a solution as well? You'll have a much better chance at getting a helpful response that way.

 

[minger]

The object floating is a sphere, so you automatically know the radius of curvature of the interaction; it's the variable you're looking for. From this and the temperature of the water, you can get the surface tension, and pressure force on the ball.

You know the mass and the area the pressure acts on. The surface tension force must be greater than the gravitational force.

 

[chamrul]

I have the very same problem:

-in order to maximize R, cos A must be 1; A=0 so that term can be left out in the eq
-in that case you have to make the assumption that you allow the ball to be half submerged.
-then the weight of metal = V(sphere) * g * p (density of metal) and let that equal to the surface tension s (N/m) acting on the equatorial circumference of the steel ball or 2*pi* R (ie set the force due to surface tension=weight of metal ball).
-solve for R and if you get anything a cm or more then you know this will not physically work

 

[ideasrule]

chamrul: you've answered the question correctly, but please don't provide detailed, step-by-step solutions to homework questions. We want to give the OP's a chance to think out problems by themselves.