# Friction question

1. May 29, 2012

### maxtor101

Hi all,

Say I have two hollow cylinders as show in the diagram. If I know the coefficient of friction between the two materials, the radii of the two cyclinders, how would I go about calculating the force to push the top cylinder over the other a distance x in t seconds?

Also assume that the bottom cylinder is open so the force required is just to overcome the friction and nothing else.

Any help is greatly appreciated!
Thank you!

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2. May 30, 2012

### Lsos

Is the opening in the larger cylinder bigger than the diameter of the smaller cylinder? Because the frictional force depends on how hard one cylinder is pressed into the other. So if the opening in the larger cylinder is larger than the smaller cylinder, frictional force should be ~0. If it's smaller, however, then indeed the cylinders will have to stretch in order to fit into each other, and the forces needed to do that can get quite large.

It's not the most simple calculation. Or, at least, I have never done it myself. I would also guess they have some sort of calculator online to help figure it out.

Whatever the size difference between the two is how much the larger one will need to expand/ smaller one will need to contract in order to fit into each other. I would figure out the size difference, and from the elasticity of the material you could figure out the force that they exert on each other. This force will rise as the cylinders move into each other, and it can get quite large very quickly depending on how much the cylinders interfere with each other.

Once you have the force, you can easily figure out how much more you need in order to achieve a distance in t seconds. Although that's a value of power, not force. And, again, it can get quite large, which means quite a bit of heat would be produced....

3. May 30, 2012

### vin300

It is a good question, but I don't think you'll ever find a good answer. We have only been taught about axial stresses and strains. We don't know of radial stresses and strains. For example, I don't think anyone can answer this question: If a steel bar of dia 30mm is compressed diametrically by 0.1mm, what is the stress applied along the circumference at the curved surface of the bar?