Conservation of energy in a wheel

[paalfis]

Homework Statement

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A wheel rolls without slipping on a plane, what magnitudes are conserved?

The Attempt at a Solution

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I don't know if the static friction force does any work. Energy won't be conserved if it does.

 

[haruspex]

Friction is a force between two surfaces in contact. When a force does work, what equation tells you how much work is done?

 

[paalfis]

Linear integral of scalar product between force and the direction of motion. But does THIS force does any work? Because after all, it is static, but its point of action is changing with time, that is my confusion.

 

[haruspex]

Linear integral of scalar product between force and the direction of motion. But does THIS force does any work? Because after all, it is static, but its point of action is changing with time, that is my confusion.

The force is 'trying' to move the surfaces in relation to each other. Does it succeed?

 

[paalfis]

No it doesn't. Ok, so energy is conserved. Energy won't be conserved if there is any slipping between the surfaces, correct?
This is not so intuitive to me because I think static force as 'pressure' applied by each body to the other body, somehow using energy to change the molecular state of the other body's structure, why is this wrong?

 

[haruspex]

Energy won't be conserved if there is any slipping between the surfaces, correct?

Correct.

I think static force as 'pressure' applied by each body to the other body, somehow using energy to change the molecular state of the other body's structure

There is some truth in that. In the case of a rolling wheel, there are losses associated with the deformation of the road and wheel as the load shifts. But this is referred to as rolling resistance, not friction. It is generally ignored in 'school', in the same way that air drag is ignored in most ballistics questions.