What is the minimum force needed to move a block with friction present?

[Dadface]

Doesn't matter. Prior to taking the test the prepared students would be familiar with FBD's. This one is so simple they could picture it in their head without drawing it. And even if they did draw it, it would take only a few seconds.

We seem agree on this point. If its understood that the minimum force cannot be bigger than mg no other FBD is needed.

But they would need to know something about $\mu$ to understand the significance of it being greater than one.

Even if there were students who didn't know about μ they could still come to the right response by looking at the four given equations. By doing so they should realize that μ is a dimensionless number and that the correct answer should apply whatever its value.

Yes. and the clever ones would take the shortcut. But only if they had previously built up a knowledge of static friction and FBD's.

You have still not addressed the pedagogical issue of how a student could reason through that shortcut without first having built up a knowledge of static friction and FBD's.

You don't need a knowledge of FBDs and static friction. You do need to know that the minimum force cannot be bigger than mg and that μ is an unspecified number.

it might seem to be a strange sort of question in that it's not really testing students knowledge of FBDs and friction but it is a multiple choice question and there would be a limited average available time for its solution.

 

[Dadface]

Mister T, I don't think we would be having this conversation if the wording of the question was more specific.

I suspect that a lot of peoples initial reaction on reading the question is that it requires one to find the minimum force needed to move the block along the surface. If that were the case students would have to apply their knowledge of FBDs and static friction.

But the question doesn't ask for the minimum force to move the block along the surface, it asks for the minimum force needed to move the block, in other words move it along, or move it up or tilt it or move it in some other way. Of course the minimum force needed to lift the block completely from the surface is mg.

 

[Dadface]

I would have liked to edit the above post by re writing the first sentence but was unable to do so. I guess there is a time limit for editing. The following is what I would have written.

Mr T, I think we wouldn't be having this conversation if the wording of the question was more specific.