Accelerating Wedge and block on top of it -- Dynamics

[andyrk]

No. When the block slides up the wedge its horizontal acceleration is less than that of the wedge. You can no longer use A for both.

How can you be so certain that the horizontal acceleration of the wedge and the block will be different? Can you prove it?

 

[haruspex]

How can you be so certain that the horizontal acceleration of the wedge and the block will be different? Can you prove it?

It's not up to me to prove it. You can't prove they're the same, so in the equations you must allow them to be different, then find out if they are.

 

[andyrk]

It's not up to me to prove it. You can't prove they're the same, so in the equations you must allow them to be different, then find out if they are.

Simply put, from what I have gathered, I have come to the conclusion that I don' t think that you can explain why the block slides up or down without involving pseudo forces in. If you know the reasoning behind something, then why don't you just say it? I am not able to figure it out myself, so there's no point in waiting and creating more confusions. And I don't even think that we can ever prove that without using pseudo forces. That is because, look at the example of a man standing on a rotating wheel. If there is no friction between his feet and the wheel, with time the man automatically goes towards the rim of the wheel due to pseudo force. There isn't any other explanation as to why this happens without using pseudo forces. Same is with the case with the wedge and block, according to me. The block slides up or down purely because of pseudo force and nothing else.

 

[haruspex]

Simply put, from what I have gathered, I have come to the conclusion that I don' t think that you can explain why the block slides up or down without involving pseudo forces in. If you know the reasoning behind something, then why don't you just say it? I am not able to figure it out myself, so there's no point in waiting and creating more confusions. And I don't even think that we can ever prove that without using pseudo forces. That is because, look at the example of a man standing on a rotating wheel. If there is no friction between his feet and the wheel, with time the man automatically goes towards the rim of the wheel due to pseudo force. There isn't any other explanation as to why this happens without using pseudo forces. Same is with the case with the wedge and block, according to me. The block slides up or down purely because of pseudo force and nothing else.

In you are standing on a rotating disk then lose friction, you will move in a straight line, at a tangent to the circle you were moving in before losing friction. You will observe this as moving towards the outer rim of the disk. This is standard Newtonian mechanics.
Pseudoforces only exist in non-inertial frames. Analysis in inertial frames and different non-inertial frames, done correctly, all lead to the same answer, therefore pseudoforces cannot be a necessary part of the explanation.
The only way you will see this is to develop the right equations and see where they lead. E.g. do not assume the horizontal accelerations are the same. I am happy to work with you on that, but don't see any other way to make progress.

 

[andyrk]

In you are standing on a rotating disk then lose friction, you will move in a straight line, at a tangent to the circle you were moving in before losing friction. You will observe this as moving towards the outer rim of the disk. This is standard Newtonian mechanics.
Pseudoforces only exist in non-inertial frames. Analysis in inertial frames and different non-inertial frames, done correctly, all lead to the same answer, therefore pseudoforces cannot be a necessary part of the explanation.
The only way you will see this is to develop the right equations and see where they lead. E.g. do not assume the horizontal accelerations are the same. I am happy to work with you on that, but don't see any other way to make progress.

Okay, so if the accelerations are different then then just the second equation changes and becomes Nsinθ = ma_x While the horizontal acceleration of the wedge and block is A. How does this account for the fact that the block slides up or down the incline depending on F?

 

[haruspex]

Okay, so if the accelerations are different then then just the second equation changes and becomes Nsinθ = ma_x While the horizontal acceleration of the wedge and block is A. How does this account for the fact that the block slides up or down the incline depending on F?

No, you cannot write A for the horizontal acceleration of 'wedge and block', since they are different.
If the wedge has the greater horizontal acceleration then the block must move up to allow the wedge to advance under it. If the block has the greater then it will descend the face of the wedge as the wedge falls behind. You can write an equation relating the three accelerations and the angle of the slope.