Why Is the Normal Force the Same on Both Blocks in a Frictional System?

[OrlandoLewis]

Homework Statement

The two blocks (m=16kg and M=88kg) are not attached to each other. The coefficient of static friction between the blocks is us=0.38, but the surface beneath the larger block is frictionless. What is the minimum magnitude of the horizontal force F required to keep the smaller block from slipping down the larger block?
(I've attached the figure in this thread)

Homework Equations

Let F be the force applied and F' be the Force of the system
F = mg/[u_s(1-[m/(m+M)])]

The Attempt at a Solution

I already know the solution to the problem but I'm having a hard time seeing why the normal force of the smaller block is equal to the total force of the whole system, not to the force applied to the smaller block.

 

[haruspex]

the total force of the whole system,

I don't know what you mean by that.
Certainly the force applied is not equal to the he normal reaction from the larger block. If it were, there would be no net force on the smaller block, so no acceleration. If the smaller block is not accelerating then the larger block is not - or the two would separate. If no acceleration of the larger block then no net force on it. No net force on it implies no force from the smaller block.

 

[OrlandoLewis]

I don't know what you mean by that.
Certainly the force applied is not equal to the he normal reaction from the larger block. If it were, there would be no net force on the smaller block, so no acceleration. If the smaller block is not accelerating then the larger block is not - or the two would separate. If no acceleration of the larger block then no net force on it. No net force on it implies no force from the smaller block.

What I mean is the force of the two block combined which is equal to their total mass multiplied by the acceleration.
Why is it equal to the horizontal normal force to the smaller block?

 

[haruspex]

What I mean is the force of the two block combined which is equal to their total mass multiplied by the acceleration.
Why is it equal to the horizontal normal force to the smaller block?

You are free to think of the two blocks as a single system. That system has an overall mass, all parts of it have the same horizontal acceleration, and there is just one external horizontal force acting on it. F=ma.

 

[TomHart]

Why is it equal to the horizontal normal force to the smaller block?

The small block appears to only have two horizontal forces. If they are equal but opposite, what is the result?

 

[OrlandoLewis]

The small block appears to only have two horizontal forces. If they are equal but opposite, what is the result?

I've attached here the free body diagram which yields the correct answer.

I doesn't really makes sense to me why the positive horizontal force F' is equal to the one horizontal force applied to the smaller block (negative direction).

 

[haruspex]

the positive horizontal force F' is equal to the one horizontal force applied to the smaller block (negative direction).

I don't understand what you mean by that. There are two forces applied to the smaller block, F and F'. F' is the reaction from the larger block, so is equal and opposite to the force on the larger block. F and F' are not equal.

 

[OrlandoLewis]

I don't understand what you mean by that. There are two forces applied to the smaller block, F and F'. F' is the reaction from the larger block, so is equal and opposite to the force on the larger block. F and F' are not equal.

Sorry for not being to specific... I hope this'll get clearer.
My question is why is F' on the left (smaller block), the same as F' on the right (larger block)...
The intuition confuses me

 

[haruspex]

Sorry for not being to specific... I hope this'll get clearer.
My question is why is F' on the left (smaller block), the same as F' on the right (larger block)...
The intuition confuses me

It is fundamental that action and reaction are equal and opposite. I cannot think of a way to make it more intuitive.