Why is static friction not considered in the work-energy theorem?

[phantomvommand]

Homework Statement

A ball rolls down a sphere (without slipping). At what height will the ball lose contact with the sphere?
Ball radius = r, sphere radius = R, ball mass = m, ball I = 2/5mr^2

Relevant Equations

Conservation of energy:
mg(R+r)(1-cos theta) = 1/2mv^2 + 1/2 I w^2.

My question is this:
- Friction exists (for no slipping/pure rolling to occur)
- Why is the work done against friction not accounted for in the conservation of energy equation?

Thank you!

 

[PeroK]

My question is this:
- Friction exists (for no slipping/pure rolling to occur)
- Why is the work done against friction not accounted for in the conservation of energy equation?

For no slipping, you have static friction, which does no work.

 

[phantomvommand]

For no slipping, you have static friction, which does no work.

Just to confirm, you mean that it does no work as the point of contact is not moving (ie Fdx = 0, as dx = 0?)

 

[PeroK]

Just to confirm, you mean that it does no work as the point of contact is not moving (ie Fdx = 0, as dx = 0?)

Yes, that's why rolling is so efficient. And why you don't lose rubber off your car tyres when drving normally.

 

[haruspex]

Just to confirm, you mean that it does no work as the point of contact is not moving (ie Fdx = 0, as dx = 0?)

It depends how you are defining dx. If as the relative motion of the surfaces then yes, dx=0.
But consider a block resting on an accelerating block, no sliding.
As far as the top block is concerned friction is doing work on it. If that block advances distance x then the work done is F_fx. The lower block takes the opposite view, i.e. the work done by the friction is -F_fx.
In short, no net work is done by static friction.