Rolling without slipping, shouldn't there be friction?

[Warlic]

A clown balances a small, spherical grape at the top of his bald head, which also has the shape of a sphere. After drawing sufficient applause, the grape starts from rest and rolls down without slipping. It will leave contact with the clown's head when the radial line joining it to the curvature makes what angle with the vertical?

This is the solution; normal force must be zero:

What I don't understand is, they say that mechanical energy is conserved. But shouldn't there be a friction force doing work on the grape as it rolls downwards?

 

[Doc Al]

But shouldn't there be a friction force doing work on the grape as it rolls downwards?

Does friction act? Yes. But does it do any work? Remember: It's rolling without slipping, so what kind of friction is it?

 

[Warlic]

Does friction act? Yes. But does it do any work? Remember: It's rolling without slipping, so what kind of friction is it?

It's going to be static friction? But then what kind of work does it do?

 

[haruspex]

What I don't understand is, they say that mechanical energy is conserved. But shouldn't there be a friction force doing work on the grape as it rolls downwards?

A force only does work if it moves something. Friction can be confusing because you need to concentrate on the surfaces in contact, ignoring whatever other motion there is. In rolling contact, the surfaces do not move relative to each other, so the friction does no work.

 

[Doc Al]

It's going to be static friction?

Right.

But then what kind of work does it do?

No kind!

 

[Warlic]

Right.No kind!

But then what makes a wheel go forwards on the ground? Isn't it friction force?

 

[Doc Al]

But then what makes a wheel go forwards on the ground? Isn't it friction force?

If it's accelerating, yes. But that doesn't mean that the friction force does work. (It can be said to do pseudowork or center of mass work, but that's more an application of Newton's 2nd law than a statement about energy.)