What force should be applied on a tile?

[zade70]

Homework Statement

On a horizontal floor there are 3 tiles on each other, 3 kg each. Which horizontal force should be applied in the middle tile, so that only it can be removed from the pile , when we know that the friction coefficient between the tiles is 0,3.

Homework Equations

F_f=[PLAIN]http://upload.wikimedia.org/math/9/3/9/939974a71dda1b83cce5ab82a2d2cec1.png*N

The Attempt at a Solution

F_f=0,3* (3+3)*10=18N, but the solution is 90N.

 

[billy_joule]

You need to consider the force applied to the other tiles.. They need to be minimized so only the middle tile is removed. As usual, you should start with a free body diagram.
Try a quick experiment with a stack of books to see what happens when you apply too small a force...

 

[haruspex]

Not sure I understand the question.
It doesn't mention friction between the bottom tile and the floor.
Since the middle tile must slide against each of the other two, we know what the frictional forces are at those interfaces. We immediately deduce the acceleration of the top tile, and it cannot be zero. So what does it mean to say that only the middle tile is removed?

• That the top and bottom tiles accelerate equally? (that requires a specific coefficient of friction, different from the given one, between tile and floor)
• That the top tile lands on the bottom tile, if somewhat offset? (that requires knowledge of tile dimensions)
• That the middle tile accelerates faster than either of the other two? (I think this gives the target answer if there's no friction on the floor, but if that's it then the question is poorly worded, or misquoted)
  
• something else?

 

[zade70]

Not sure I understand the question.
It doesn't mention friction between the bottom tile and the floor.
Since the middle tile must slide against each of the other two, we know what the frictional forces are at those interfaces. We immediately deduce the acceleration of the top tile, and it cannot be zero. So what does it mean to say that only the middle tile is removed?

• That the top and bottom tiles accelerate equally? (that requires a specific coefficient of friction, different from the given one, between tile and floor)
• That the top tile lands on the bottom tile, if somewhat offset? (that requires knowledge of tile dimensions)
• That the middle tile accelerates faster than either of the other two? (I think this gives the target answer if there's no friction on the floor, but if that's it then the question is poorly worded, or misquoted)
  
• something else?

These are the problem data. The answer is 90N. Could you relate the answer to it?

 

[haruspex]

These are the problem data. The answer is 90N. Could you relate the answer to it?

No, I can't find any interpretation that reaches an answer of 90N.
But I gave you two interpretations which at least allow an answer to be calculated. Why don't you have a go at those and confirm my results?

• That the top and bottom tiles accelerate equally. (Allow for friction with the floor, different coefficient.)
• That the middle tile accelerates faster than either of the other two, no friction with the floor.