Is the Maximum Radius of a Wire Floating on Liquid Affected by Surface Tension?

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Homework Help Overview

The discussion revolves around the maximum radius of a wire that can float on a liquid surface, considering the wire's density and the liquid's surface tension. The problem is situated within the context of fluid mechanics and surface tension effects.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between the wire's radius, density, and the surface tension of the liquid. Questions arise regarding the forces acting on the wire, including gravitational force and the force due to surface tension. Some participants also express confusion about the calculations leading to differing results from a reference source.

Discussion Status

The discussion includes attempts to derive a formula for the maximum radius of the wire based on given parameters. Some participants have provided calculations and expressed uncertainty about discrepancies with textbook answers. There is no explicit consensus on the correctness of the solutions presented.

Contextual Notes

Participants note the specific values for density and surface tension, as well as the assumption that the wire is not wetted by the liquid. There is mention of a potential error in the reference material, which adds to the complexity of the discussion.

Amith2006
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Sir,
The material of a wire has a density of 1.4 gm/cc. If it is not wetted by a liquid of surface tension of 44 dyne/cm, then what is the maximum radius of the wire that can float on the surface of the liquid?
Can you give a hint to solve this problem?
 
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Amith2006 said:
Sir,
The material of a wire has a density of 1.4 gm/cc. If it is not wetted by a liquid of surface tension of 44 dyne/cm, then what is the maximum radius of the wire that can float on the surface of the liquid?
Can you give a hint to solve this problem?
What is the force of gravity (per cm) on the wire as a function of its radius? What is the force (per cm) required to overcome the surface tension?

AM
 
Amith2006 said:
Sir,
The material of a wire has a density of 1.4 gm/cc. If it is not wetted by a liquid of surface tension of 44 dyne/cm, then what is the maximum radius of the wire that can float on the surface of the liquid?
Can you give a hint to solve this problem?
I solved it in the following way:
Let the radius, density and length of the wire be r, d and l respectively. Let T be surface tension.
Mass per unit length of the wire = volume x density
= (pi) x (r^2) x d
Force per unit length of the wire = (pi)(r^2)d x g (g ~ 1000 cm/sec^2)
By definition of surface tension,
Force per unit length of the wire = surface tension
(pi)(r^2)d x g = T
r^2 = T/[(pi) x d x g]
By solving I get,
r =1/10 cm
But the book answer is 10/7 cm. Is there any mistake in my solution?
 
Amith2006 said:
I solved it in the following way:
Let the radius, density and length of the wire be r, d and l respectively. Let T be surface tension.
Mass per unit length of the wire = volume x density
= (pi) x (r^2) x d
Force per unit length of the wire = (pi)(r^2)d x g (g ~ 1000 cm/sec^2)
By definition of surface tension,
Force per unit length of the wire = surface tension
(pi)(r^2)d x g = T
r^2 = T/[(pi) x d x g]
By solving I get,
r =1/10 cm
But the book answer is 10/7 cm. Is there any mistake in my solution?
Your answer appears to be correct. A metal wire 1.4 cm thick will not float on water. Again, your book is wrong.

AM
 
Last edited:

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