Equilibrium of Two Blocks in a Wall System: A FBD Approach

[rudransh verma]

Homework Statement

All the surfaces shown are rough and the system is in equilibrium. The direction of friction on B due to A is-

Relevant Equations

F=ma

This problem is similar to what I have done before here. I think since the system is in equilibrium, that is both bodies are at rest, net force on each should be zero. So to balance the forces in all directions we need only friction forces on each in upward direction. So the force on B due to A is upwards.

 

[BvU]

As a free body diagram will make clear !

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[Doc Al]

Homework Statement:: All the surfaces shown are rough and the system is in equilibrium. The direction of friction on B due to A is-
Relevant Equations:: F=ma

I think since the system is in equilibrium, that is both bodies are at rest, net force on each should be zero.

So far, so good.

Homework Statement:: All the surfaces shown are rough and the system is in equilibrium. The direction of friction on B due to A is-
Relevant Equations:: F=ma

So to balance the forces in all directions we need only friction forces on each in upward direction.

What about Newton's third law?

Homework Statement:: All the surfaces shown are rough and the system is in equilibrium. The direction of friction on B due to A is-
Relevant Equations:: F=ma

So the force on B due to A is upwards.

Don't guess. Work it out step by step. As @BvU advises, start with a free body diagram. Do a diagram for each block.

 

[rudransh verma]

What about Newton's third law?

I don't think its correct since there is more force downwards than upwards.

 

[BvU]

' For each block ' is pretty unambiguous!

That way you can untangle the mess you now have between A and B.

And perhaps you need a FBD for the wall too

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[Doc Al]

I don't think its correct since there is more force downwards than upwards.

Do you seriously think Newton's 3rd law doesn't apply here? Draw a free body diagram for each block.

 

[rudransh verma]

Do you seriously think Newton's 3rd law doesn't apply here? Draw a free body diagram for each block.

 

[Doc Al]

For block B, describe each force you show. On the left of the block, you show a force going up and a force going down. What are they supposed to be?

 

[rudransh verma]

For block B, describe each force you show. On the left of the block, you show a force going up and a force going down. What are they supposed to be?

I am unable to decide which body applies friction up and which body applies down.

 

[Doc Al]

I am unable to decide which body applies friction up and which body applies down.

Just pick a direction and see what Newton says about it. You know each body is in equilibrium. Focus on block B.

 

[rudransh verma]

Just pick a direction and see what Newton says about it. You know each body is in equilibrium. Focus on block B.

I will start from the wall . All is balanced for A. Now due to weight of B it applies downward force on A and inreturn A applies upwards on B.

 

[Doc Al]

I will start from the wall .

OK, but you'll find the answer you need quicker if you start with B.

All is balanced for A.

OK. Forces are balanced for both A and B.

Now due to weight of B it applies downward force on A and inreturn A applies upwards on B.

Careful. The weight of B (the force of gravity) acts only on B. There is a force that B exerts on A (friction) and A exerts an equal and opposite friction force on B. (They are 3rd law pairs.)

But your diagram is much better now!

 

[rudransh verma]

Careful. The weight of B (the force of gravity) acts only on B. There is a force that B exerts on A (friction) and A exerts an equal and opposite friction force on B. (They are 3rd law pairs.)

It doesn’t feel right though. A has more downward force than upwards. How is it going to stay in equilibrium?

 

[Doc Al]

A has more downward force than upwards.

Why do you think that? Just because there are two forces acting down and only one acting up?

How is it going to stay in equilibrium?

All the forces must balance. What does that tell you?

 

[rudransh verma]

All the forces must balance. What does that tell you?

Well it tells that friction of wall is much greater than weight and force from B.
There should be a beginning point in these kind of problems otherwise I feel I will get lost. Like here I started with wall.

 

[Doc Al]

Well it tells that friction of wall is much greater than weight and force from B

Really? So you think A is accelerating up the wall? (If you think the upward force is greater than the downward force, that's what you must conclude.)

What it should tell you is that the upward friction force from the wall must just balance the downward forces acting on A.

 

[kuruman]

Here is a thought: The blocks don't know (or care to know) whether they are up against a wall or another block. So the force of friction exerted by A on B is in the same direction as the force of friction exerted by the wall on A. Does this help you sort out the directions of Newton's 3rd law pairs?

 

[BvU]

How about doing the exercise without $F$ and with glue instead of friction ?
What Would the FBDs be ?

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[rudransh verma]

Careful. The weight of B (the force of gravity) acts only on B. There is a force that B exerts on A (friction) and A exerts an equal and opposite friction force on B. (They are 3rd law pairs.)

I have a doubt which I didn’t sort and ignored.

The force of weight acts downward on B which will tend to pull it down and this will be opposed by friction from A. So, an upward force acts on B by A. And B exerts an equal and opposite force on A.
Same result but this explanation seems right.

Is there a starting point here like not starting from wall but from body B when drawing FBD?

 

[Doc Al]

Is there a starting point here like not starting from wall but from body B when drawing FBD?

Of course. All you need to answer the question is a FBD of body B.

That's what I tried to get you to do when I said above:

Focus on block B.

If you start from the wall, you're doing unnecessary work. But it's good to do anyway to deepen your understanding.