Stacked blocks pulled horizontally

[judas_priest]

Homework Statement

Two blocks of equal masses are placed on a horizontal table as shown. The bottom block is then pulled with a slowly increasing horizontal force F. The coefficients of static friction for both surfaces are greater than zero and equal to each other.

Here are the options:

A ) The top block begins to move as soon as F reaches a certain minimum value; the bottom block would never move even as F increases further.

B) The top block begins to move as soon as F reaches a certain minimum value; the bottom block does not move at that instant but would begin to move as F increases further.

C) Both blocks begin to move simultaneously as F reaches a certain minimum value; as F increases further, the acceleration of the bottom block exceeds the acceleration of the top block.

D) The bottom block begins to move as soon as F reaches a certain minimum value; the top block would never move even as F increases further.

E) The bottom block begins to move as soon as F reaches a certain minimum value; the top block does not move at that instant but would begin to move as F increases further. Status: incorrect

F) Both blocks begin to move simultaneously as F reaches a certain minimum value; as F increases further, both blocks always have the same acceleration.

G) Both blocks begin to move simultaneously as F reaches a certain minimum value; as F increases further, the acceleration of the top block exceeds the acceleration of the bottom block.

The Attempt at a Solution

On drawing FBD, the bottom block has three forces i.e external force, friction between block and ground, and the reaction friction force of top block.

On drawing FBD for top block, there's only one force that is friction between the two blocks. I don't know how to proceed from here. Is there physics involved? I think it's more of a logic question.

 

[darkxponent]

Hint: What is the property of Friction. How does it change with F?

 

[haruspex]

On drawing FBD, the bottom block has three forces i.e external force, friction between block and ground, and the reaction friction force of top block.

I count three more.

On drawing FBD for top block, there's only one force that is friction between the two blocks.

Two more

Is there physics involved? I think it's more of a logic question.

Physics is logical, and any reasoning applied would invoke the physics, so there's not really a difference. If you mean, should you be writing equations, it would help.

 

[judas_priest]

Friction's a self adjusting force. Increases with increase in force. I've gone through all of it. I think this question is more logic than physics.

 

[darkxponent]

Is there physics involved? I think it's more of a logic question.

There is lot of physics involved in it and physics is purely Logic!

 

[judas_priest]

@haruspex, I ignored the vertical forces since they don't play much of a role in this question.

 

[darkxponent]

Friction's a self adjusting force. Increases with increase in force. I've gone through all of it. I think this question is more logic than physics.

What type of friction is acting, static or dynamic. What is the difference between them? What is the formula for static friction? What is the formula for dynamic Friction?

As haruspex said, you just ignored important Forces in drawing the FBDs. Count them all!

 

[judas_priest]

Okay, for the bottom block to move, the force required would be F = 2*mu*m*g - mu*m*g.
For the block on the top it would be mu*m*g.
Therefore, the force required for both the blocks is the same, hence they'd both move together. Is that correct?

 

[darkxponent]

Okay, for the bottom block to move, the force required would be F = 2*mu*m*g - mu*m*g.
For the block on the top it would be mu*m*g.
Therefore, the force required for both the blocks is the same, hence they'd both move together. Is that correct?

No this is not correct. I said something about the static friction, you ignored that. Draw FBD and look how the blocks friction values will change with F, as F is increasing.

You can have a small demonstration of the problem. If you have two books with you right now. Put one on another. Do these steps. Hopefully you will get the result.

1. Pull the bottom one with very little or no Force.
2. Pull the bottom one with slightly more Force.
3. Pull the bottom one very quickly.

Then try solving the equations made from FBDs.

Hint: The values of Friction you are taking in wrong. It depends on F.

 

[judas_priest]

I think I'll stick to doing it theoretically since I can't find two blocks and a surface or 3 same blocks with with same surface.

Anyways, How are the forces is wrong. Normal force for the bottom most block is 2Mg, Therefore friction to the left is 2*mu*mg and to the right because of the reaction of top block's friction is mu*mg. Hence the force required is F = mu*mg.

For the Top block is also the same because there is friction of mu*mg acting towards left. Hence force required would remain F mu*mg.

Where am I going wrong?

 

[darkxponent]

Where am I going wrong?

I have repeatedly told you. You are taking the values of Friction wrong. .

F_static ≤ μN

F_dynamic = μN

Dynamic Friction will only occur when there is a relative movement between two surfaces. Otherwise, it is just the static friction which resists the motion, by balancing the applied Force till the net applied Force is less than μN, once the value of applied force exceeds the limiting Friction value that is μN, the surfaces start moving relative to each other.

 

[darkxponent]

I think I'll stick to doing it theoretically since I can't find two blocks and a surface or 3 same blocks with with same surface.

Same surfaces doesn't matter. You will still get the same result. Try the demonstration, it will hardly take 10 seconds! It always interesting to understand physics observing phenomenon around us

 

[judas_priest]

Exactly my point. If the force exceeds mu*mg, both surfaces start moving, because the max value of static friction is 2mu*mg for the lower block, but there's a reaction from top block's friction of mu*mg that makes the required force to make the bottom block break into motion as mu*mg (Because at this force, it exceeds the value of static friction). And the min value for top block to break into motion is F= mu*mg, because that's the amount of force required to exceed the value of static friction for top block.

 

[judas_priest]

Same surfaces doesn't matter. You will still get the same result. Try the demonstration, it will hardly take 10 seconds! It always interesting to understand physics observing phenomenon around us

Same surfaces VERY much matters because coefficient of friction depends on material of two bodies.

 

[judas_priest]

Okay, so I did the experiment anyway, and the answer would be

Both blocks begin to move simultaneously as F reaches a certain minimum value; as F increases further, the acceleration of the bottom block exceeds the acceleration of the top block.

Can you explain the mechanics?

 

[darkxponent]

Exactly my point. If the force exceeds mu*mg, both surfaces start moving, because the max value of static friction is 2mu*mg for the lower block, but there's a reaction from top block's friction of mu*mg that makes the required force to make the bottom block break into motion as mu*mg (Because at this force, it exceeds the value of static friction). And the min value for top block to break into motion is F= mu*mg, because that's the amount of force required to exceed the value of static friction for top block.

Both blocks will start moving when F exceeds 2μmg. Think both blocks as a system. The Friction is acting backward for the system at the lower surface.

but there's a reaction from top block's friction of mu*mg

Wrong. The two surfaces are still moving together. How did you take the dynamic value of friction. The friction acting is static.

 

[judas_priest]

Wrong. The two surfaces are still moving together. How did you take the dynamic value of friction. The friction acting is static.

Why is it static, can you explain? Give a reason to support your answer. By the mechanics.

 

[darkxponent]

Okay, so I did the experiment anyway, and the answer would be

Both blocks begin to move simultaneously as F reaches a certain minimum value; as F increases further, the acceleration of the bottom block exceeds the acceleration of the top block.

Can you explain the mechanics?

The results of the experiment are correct. Now redraw the FBD. Do not take the values of friction constant. Take the values of friction f1, f2. Now use the constraints

f1≤ μmg
f2≤ 2μmg

Show the equation to me.

 

[judas_priest]

For the lower block, F = f2 - f1
For the upper block, F = f1
These are for the horizontal direction.

For the lower block, F = Mg + N1(due to upper block) - N2(due to earth)
For the lower block, F = Mg - N1(due to lower block)
These are for the vertical direction

 

[darkxponent]

Why is it static, can you explain? Give a reason to support your answer. By the mechanics.

I did not talk about circuits anywhere!. I am talking mechanics only. At the surface between the blocks, the Lower block has tendency to move forward, but as is the property of friction, which does exist between the two blocks, Friction opposes the motion of the lower block, so it applies a force on lower block backward, means that the upper block exerts a force on the lower block backwards. Then Newtons Third Law comes into play and the lower block exerts an equal amount of Force on the upper block in the opposite direction that is forward direction. This Friction f1 will be static until the two surfaces don't move relative to each other.

 

[judas_priest]

Friction opposes the motion of the lower block, so it applies a force on lower block backward, means that the upper block exerts a force on the lower block backwards. Then Newtons Third Law comes into play and the lower block exerts an equal amount of Force on the upper block in the opposite direction that is forward direction. This Friction f1 will be static until the two surfaces don't move relative to each other.

I think you meant it the other way round. The upper block exerts a frictional force on lower block forward which is due to the reaction of lower block exerting a frictional force on upper block backward.

 

[darkxponent]

For the lower block, F = f2 - f1
For the upper block, F = f1

Did you mean.

For the upper block Net Force = f1, Correct.

For the upper block there is an external force, that is given in the problem, including f2 and f1 you misses it.

no need for vertical Forces here execpt for they will be only used in finding values of f1 and f2.

 

[haruspex]

F_static ≤ μN
F_dynamic = μN

Strictly speaking, of course, F_static ≤ μ_staticN ≥ μ_dynamicN = F_dynamic. But the OP doesn't mention μ_dynamic. I believe the answer is the same taking the strict view, but the reasoning gets a little more complex.

 

[darkxponent]

I think you meant it the other way round. The upper block exerts a frictional force on lower block forward which is due to the reaction of lower block exerting a frictional force on upper block backward.

You can understand it taking any block as reference, it hardly matters. The result is however the same.

 

[judas_priest]

Did you mean.

For the upper block Net Force = f1, Correct.

For the upper block there is an external force, that is given in the problem, including f2 and f1 you misses it.

no need for vertical Forces here execpt for they will be only used in finding values of f1 and f2.

I can't think of any other force on upper block.
The external force is on the lower block.

 

[darkxponent]

Strictly speaking, of course, F_static ≤ μ_staticN ≥ μ_dynamicN = F_dynamic. But the OP doesn't mention μ_dynamic. I believe the answer is the same taking the strict view, but the reasoning gets a little more complex.

Yes it would be more complex if μ_static and μ_dynamic were different, but generally when not given in problem we take μ_static = μ_dynamic. How ever only mathematical values would be effected. And for the type of question given by OP, the result would be same in both case.

 

[judas_priest]

Okay, but I still haven't got the answer as to why upper block stays with lower block upto a certain value and then falls behind.
Can we conclude this?

 

[darkxponent]

I can't think of any other force on upper block.
The external force is on the lower block.

It was a typo error, i was writing lower! Anyways now you can show me the equation for lower block.

 

[darkxponent]

Okay, but I still haven't got the answer as to why upper block stays with lower block upto a certain value and then falls behind.
Can we conclude this?

No, because just helping you solve the problem is not the motive of PF. You should understand the concept cleanly, mathematically, so that you can solve any similar problem, or more complex one like one stated by haruspex, yourselves. You are very close just form the equations from the FBDs.

 

[judas_priest]

No, because just helping you solve the problem is not the motive of PF. You should understand the concept cleanly, mathematically, so that you can solve any similar problem, or more complex one like one stated by haruspex, yourselves. You are very close just form the equations from the FBDs.

Are my FBDs correct? Where am I going wrong?

 

[judas_priest]

Here's another question. What if the lower block had an external force towards right, with friction between two blocks remaining, but no friction between lower block and ground.

 

[darkxponent]

Are my FBDs correct? Where am I going wrong?

You didn't show any FBD, did you?, so how can they be correct or incorrect. Show the two FBD, now you know well the Forces acting on the two blocks.

Here's another question. What if the lower block had an external force towards right, with friction between two blocks remaining, but no friction between lower block and ground.

This is or more or less the same question as OP. Solve the first one and put the value of μ_ground = 0.

 

[judas_priest]

You didn't show any FBD, did you?, so how can they be correct or incorrect. Show the two FBD, now you know well the Forces acting on the two blocks.



This is or more or less the same question as OP. Solve the first one and put the value of μ_ground = 0.

I've shown my FBDs 3 times now. You've even responded to them.

 

[judas_priest]

I'm going to post the diagram with forces for the question I just asked (i.e What if the lower block had an external force towards right, with friction between two blocks remaining, but no friction between lower block and ground.). Let me know if I'm doing it right.

 

[darkxponent]

I've shown my FBDs 3 times now. You've even responded to them.

You have posted just one attachment to this thread, that is the diagram of the question. I haven't find any attachment of Free Body Diagrams.