# Work done by static friction? Conveyor belt vs frictionless lego pieces

Theoretically (I thought) static friction does no work. Practically, this answer says it does and it's using a conveyor belt as an example.

My question here is: In the conveyor belt case, are the groceries moved by the friction force? Or by the belt, and the static friction is just a way of interlocking the groceries onto the belt.
To emphasize my point l, I'd like to use an example of two lego pieces made of some frictionless material stacked up on top of each other, interlocked by their shape and the gravity. If we move the bottom piece and it in turn moves the upper piece, would it be correct to say that the shape or the interlocking system moved the upper piece? Or can we simply state that the bottom piece moved the upper piece and by doing so sticking to the idea that static friction does no work (?)
We can go even further with the shape vs friction. We can take a cubical block of frictionless material and a U-shaped piece of same material. The U-shaped piece pushes the cube on a table slightly upwards. Can we still say that the way the two interlock and are able to move each other is somehow called friction?

Or a spoon pushing a small ball upward?

I mean at what point do we start saying that the one object pushed the other instead of "the friction" ?

• For the conveyor belt problem, I think the work done on the block will be by the static friction. The work done on the belt itself will be done by a motor. The motor does not do any work on the block because it is not in contact with the block. Commented Jan 4, 2019 at 5:07
• If your legos are made of frictionless material, then moving one, would not move the second one.
– Rick
Commented Feb 17, 2019 at 14:29

The amount of work done by a force is a frame-dependent quantity.

Consider this:

• Place a box on a level surface that you are standing on, then push gently on the box such that you do not overcome the friction. You can easily conclude that static friction does no work on the box. And you also do no work on the box.

• But look around and notice that your level surface is a moving beltway. People standing nearby can (almost as easily) compute that the static friction does non-zero work on the box1. And that you do work on the box as well, but the two quantity cancel out so that the box maintains a constant speed.

So phrases like "static friction does no work" have a interesting place: they are fundamentally misguided, but they are also useful rules of thumbs for simple problems addressed in the "obvious" frame.

Aside: An interesting exercise related to this observation is to convince yourself that if the Work-Energy Theorem is satisfied in one inertial frame it is also satisfied in other inertial frames.

1 So long as the direction of your push is not perpendicular to the direction of the belt's motion relative them.

If friction is the mechanism that "interlocks" the 2 then it is the cause of force. Why would static friction do no work? What is causing you to think that? The term static, or the numerous examples of blocks being pushed on rough surfaces. In this example the belt is moving with the object on it. It is doing the work. The lego example you have given is exactly how we describe friction at the micro level.

• I guess I was challenging the notion of "friction" itself :) Commented Jan 4, 2019 at 9:21