Discussion on an easy MCQ problem

[neelakash]

Just a few hours ago,I have posted a problem in the homework section.Here I want to discuss a similar problem---I mean the interpretation of the answer of a similar problem.

A block is placed against a vertical wall,and another block is placed against this block.We apply a horizontal external force F on the outer block(which is far from the wall) and the system is in equilibrium.Masses are not known.All the surfaces are rough...but the friction co-eff is(are?) not known.

The question asks to find the direction of frictional force on the outer block by the inner block.By no ambiguity it is upward.

This means the reverse frictional force on the inner block(nearesr to the wall) is downward.This also means relative to the outer block, the inner block tends to move upwards!I wanted to visualize this point in a physical way.

In fact,I want to analyze this point...Note that we can write down the force equations as μ₁F=W+μ₂F where μ₁ is the fr coeff at the wall and μ₂ is the same at the contact of the two blocks...

This means (μ₁-μ₂)F=W and (μ₁-μ₂)=W/F [it should be clear if μ₁=μ₂,we are in trouble.
What if W>>F?

Note that the problem specifies no constraint.but I am wondering of the problem is valid at all if W>>F,because in that case we are at a mess...Normally,μ s are typically of the order of 0.2-0.8...The problem specifies nothing about the relative magnitudes of F,W etc...is not the problem in a sense incomplete?

One can say that we are already told that the sysytem is in equilibrium.So,we are to think like this...

I cannot accept it whole heartedly...if you start looking at the free body diagram of the outer body,you can jump at the correct conclusion about the direction of friction onto it.But if you start from that of the inner body...it will trouble you.And you get the opposite conclusion...

Whatever way may I approach,the final answer should be unambiguous...
Please show me if I am making some mistake...

 

[Doc Al]

The question asks to find the direction of frictional force on the outer block by the inner block.By no ambiguity it is upward.

This means the reverse frictional force on the inner block(nearesr to the wall) is downward.This also means relative to the outer block, the inner block tends to move upwards!I wanted to visualize this point in a physical way.

Very good. Perhaps it's easier to visualize it in reverse: With respect to the inner block, were there no friction between the blocks the outer block would slide down.

In fact,I want to analyze this point...Note that we can write down the force equations as μ₁F=W+μ₂F where μ₁ is the fr coeff at the wall and μ₂ is the same at the contact of the two blocks...

One thing to beware of: When talking about static friction, remember that μ₁F is the maximum possible friction force--but the actual value of the friction could be anything from zero up to that maximum. Static friction is whatever it needs to be to prevent slipping--up to its maximum value. You can't just assume it's equal to μF.

This means (μ₁-μ₂)F=W and (μ₁-μ₂)=W/F [it should be clear if μ₁=μ₂,we are in trouble.
What if W>>F?

Note that the problem specifies no constraint.but I am wondering of the problem is valid at all if W>>F,because in that case we are at a mess...Normally,μ s are typically of the order of 0.2-0.8...The problem specifies nothing about the relative magnitudes of F,W etc...is not the problem in a sense incomplete?

This much is true: μ₂F must be at least as great as the weight of the outer block and μ₁F must be at least as great as the weight of both blocks together. Otherwise equilibrium cannot be had.

But it's often the case that you can make deductions about one aspect of a problem with very little information. So, for what it asks, the problem is "complete"--meaning you have all the information to deduce the answer. You may not have enough information to answer other questions, which may have provided a second route to your first answer.

(What does MCQ stand for?)

 

[neelakash]

One thing to beware of: When talking about static friction, remember that μ₁F is the maximum possible friction force--but the actual value of the friction could be anything from zero up to that maximum

Yes,you are correct,I seemed to forget this.So,the upward friction must be equal to the total force,but not necessarily μ₁F.Much of my confusion came from the expression of
(μ₁-μ₂)...

I do not know the full name of MCQ but it would be nice if the problem could be done from the inner block...