Friction on inclined planes

[Bipolarity]

Homework Statement

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Homework Equations

The Attempt at a Solution

I want to first make sure I understand the problem properly. Please verify each of my statements. If there is no force F acting on the (large) triangular block, then the large triangular block will move to the right. The small triangular block will slide down the large block depending on the coefficient of static friction. If the static friction is strong, the small block will stay put. If friction is too weak, the block will slide down the larger one. So far, so good?

Once the force F acts on the large block, the situation is chaged. Now the forces acting on the large bock are:
- Gravity
- F
- Normal force due to surface between floor and large block
- Reaction force due to normal force due to surface between large and small block

Forces acting on the small block:
- Gravity
- Normal force due to surface between large and small block
- Frictional force due to friction in the surface between large and small block

Is this correct so far?
Next, having defined all the forces present, I want an intuitive understanding of the acceleration of each block. Obviously this will depend on F, but assuming we know F, can we correctly say that the large block will accelerate to the left with a certain acceleration we can calculate, and that the small block will accelerate up the large block? I am a bit confused about the smaller block's motion.

What are we solving for in this problem? Also, please read between the lines of my post and post accordingly. My main confusion regards the interdependence between F, the large block, and the small block.

All help is appreciated. Thanks.

BiP

 

[mfb]

I want to first make sure I understand the problem properly. Please verify each of my statements. If there is no force F acting on the (large) triangular block, then the large triangular block will move to the right. The small triangular block will slide down the large block depending on the coefficient of static friction. If the static friction is strong, the small block will stay put. If friction is too weak, the block will slide down the larger one. So far, so good?

[Forces]
Is this correct so far?

Right

Next, having defined all the forces present, I want an intuitive understanding of the acceleration of each block. Obviously this will depend on F, but assuming we know F, can we correctly say that the large block will accelerate to the left with a certain acceleration we can calculate, and that the small block will accelerate up the large block? I am a bit confused about the smaller block's motion.

The small block should be "on the verge of sliding up" - but still stationary (relative to the large block). This simplifies the analysis, as both blocks move in the same way.

What are we solving for in this problem?

The required force F.

 

[Bipolarity]

Right


The small block should be "on the verge of sliding up" - but still stationary (relative to the large block). This simplifies the analysis, as both blocks move in the same way.


The required force F.

I don't understand what "on the verge of sliding up" means. What does that mean physically, and mathematically, does it mean that the frictional force on the small block cancels out with the gravitational component on the small block parallel to the surface between the large and small block?

What is the net acceleration of the large block intuitively? Is it 0, or is it the same as that of the large block? I am very confused on these matters. Would appreciate further clarification thanks.

BiP

 

[mfb]

If you would increase F a tiny bit, the block would slide upwards.
Therefore, the static friction is maximal in your setup (and pointing down the incline).

What is the net acceleration of the large block intuitively? Is it 0, or is it the same as that of the large block?

I assume that you mean "small block"?
It is the same as the large block.

 

[Nickie]

Your understanding of the problem is correct. The large block will move to the right if there is no force acting on it, and the small block will slide down the large block depending on the coefficient of static friction between them. When a force F is applied to the large block, the forces acting on it are gravity, the applied force F, the normal force due to the surface between the floor and the large block, and the reaction force due to the normal force between the large and small block. The forces acting on the small block are gravity, the normal force between the large and small block, and the frictional force between them.

To understand the motion of the blocks, we can use Newton's Second Law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. In this case, the large block will have a net force to the left (due to the applied force F) and the small block will have a net force upwards (due to the normal force and frictional force). The acceleration of each block can then be calculated using the net force and the mass of the block.

In this problem, we are solving for the acceleration of each block and the coefficient of static friction between the large and small block. The interdependence between F, the large block, and the small block is that the applied force F will affect the acceleration of the large block, which in turn will affect the normal force and frictional force between the large and small block, ultimately determining the motion of the small block. It is important to consider all the forces and their interrelationships in order to accurately solve the problem.

I hope this helps clarify the problem and your understanding. Good luck with your homework!