Is the Work Done by Static Friction Always Zero in a Round Trip?

[jbriggs444]

If there is no slippage, then we treat the turntable-coin system as a rigid body. We analyze rigid bodies as a whole with it's CG and moments of inertia. We can do work on the system.

I suppose one could analyze it one atom at a time with all the interatomic forces, but what's the point?

You already split the problem into a coin and a turntable. One can draw a boundary there and ask about the work done across the boundary. No need to worry about molecules.

If you are going to ask a question about work done across an interface, do not object when someone answers your question.

 

[A.T.]

If it is static, there is no distance.

Distance is frame dependent, and so is the work done by static friction. You are misunderstanding what "static" means here.

 

[A.T.]

Static friction IS static in reference to the objects in contact.

Or rather in the rest frame of the contact patches. But in other frames static friction can do work.

 

[anorlunda]

In the reference frame of the interface between two surfaces, static friction does no work, because there is never displacement between the surfaces. In the same reference frame, kinetic friction is always in the direction opposite the motion, and does negative work.[64] However, friction can do positive work in certain frames of reference. One can see this by placing a heavy box on a rug, then pulling on the rug quickly. In this case, the box slides backwards relative to the rug, but moves forward relative to the frame of reference in which the floor is stationary. Thus, the kinetic friction between the box and rug accelerates the box in the same direction that the box moves, doing positive work.[65]

Are you guys saying that if the coin is attached by welding rather than friction the coin still does work in certain reference frames?

Are you rejecting the model of the coin-turntable system as a single rigid body?

 

[anorlunda]

You already split the problem into a coin and a turntable. One can draw a boundary there and ask about the work done across the boundary. No need to worry about molecules.

Distance is frame dependent, and so is the work done by static friction. You are misunderstanding what "static" means here.

I'm feeling dense, not understanding what you're saying.

With static friction, there is no motion between the two objects. Relative motion is the only thing that differentiates static friction from kinetic friction.

The coin moves zero displacement relative to the turntable. Zero distance remains zero in all frames of reference.

 

[jbriggs444]

Are you guys saying that if the coin is attached by welding rather than friction the coin still does work in certain reference frames?

Yes.

Are you rejecting the model of the coin-turntable system as a single rigid body?

No. It seems that you are rejecting the model of the coin-turntable system as having two bodies and, thus, rejecting the notion that there is any force in the first place.

 

[jbriggs444]

I'm feeling dense, not understanding what you're saying.

With static friction, there is no motion between the two objects. Relative motion is the only thing that differentiates static friction from kinetic friction.

The coin moves zero displacement relative to the turntable. Zero distance remains zero in all frames of reference.

The force of the coin on turntable is non-zero in all frames of reference.
The point where coin touches turntable has non-zero displacement in some frames of reference.
The force of coin on turntable does work in some frames of reference.

A correct point that you may be trying to make is that a static frictional 3rd law force pair does zero total work because the two component forces act at all times in equal and opposite directions on points of action that move identically. The force that A.T. and I are discussing is only one member of such a pair.

The force of turntable on coin does equal and opposite work in all frames of reference.

 

[sophiecentaur]

Who is going to blink first on this one?
No work is done ON the material which comprises the join between the two non slipping surfaces but, just as the person pushing is doing work and the final target of the work is having work done on it, you can say that the coin (or whatever) is 'doing work' on the rest of the chain.
It would be daft to say that the only places that work can be considered to be done is at two arbitrary points (the hand of the operator or the valve on the steam whistle).
Dressing it all up with Reference Frames and Third Law pairs is actually clouding the issue, rather than making it clearer. The fact is that Energy is transferred from somewhere to somewhere else by mechanical forces. It passes through every point in the chain.
Every force is one of a third law pair and those pairs are all the way along the chain. etc. etc.
Why don't both sides consider themselves 'right' and realize that this discussion has been done to death?

 

[jbriggs444]

Who is going to blink first on this one?
No work is done ON the material which comprises the join between the two non slipping surfaces

Agreed. In principle anyway -- in the limit of focusing in tightly enough that the mass of said material is negligible. And counting the forces in both directions.

just as the person pushing is doing work and the final target of the work is having work done on it, you can say that the coin (or whatever) is 'doing work' on the rest of the chain.

Agreed.

It would be daft to say that the only places that work can be considered to be done is at two arbitrary points (the hand of the operator or the valve on the steam whistle).

Agreed. One can divide up complex mechanisms into component systems in lots and lots of ways. Accordingly, there are lots and lots of places where work can be considered to be done.

Dressing it all up with Reference Frames and Third Law pairs is actually clouding the issue, rather than making it clearer. The fact is that Energy is transferred from somewhere to somewhere else by mechanical forces. It passes through every point in the chain.

Agreed. Though, perhaps surprisingly, the direction in which energy passes along a particular chain can be frame dependent!

[I'll try not to argue about whether reference frames cloud or clear things]

Why don't both sides consider themselves 'right' and realize that this discussion has been done to death?

I shall try.

 

[sophiecentaur]

I shall try.

Go on go on go on. You know you want to.

Though, perhaps surprisingly, the direction in which energy passes along a particular chain can be frame dependent!

Oh yes. A car skidding to a halt or a car accelerating in reverse, and many others.

 

[anorlunda]

A correct point that you may be trying to make is that a static frictional 3rd law force pair does zero total work because the two component forces act at all times in equal and opposite directions on points of action that move identically. The force that A.T. and I are discussing is only one member of such a pair.

OK maybe we can agree with that definition.

 

[sophiecentaur]

Group hug now.

 

[A.T.]

The coin moves zero displacement relative to the turntable.

Yes.

Zero distance remains zero in all frames of reference.

No. In frames where the coin moves the distance it travels is not zero.