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A box sits on a table at rest and is not about to move. Which one of the following is a correct statement?

a) The normal reaction of the table on the box is equal to the mass of the box

b) The friction force on the box is equal to the coefficient of friction multiplied by the normal reaction

c) The friction force on the box is positive

d) The normal reaction of the table on the box is equal to the weight of the box.

It is clear to me that a) and c) are incorrect, which leaves me b) and d). In the end, I chose the correct answer d).

But my question is what makes b) incorrect? I looked at the answers and it says that b) is incorrect because the box is not about to move so there is no friction force on it. What?

Shouldn't the reason that the box is not moving because of the friction force preventing it from moving? If so why can't I calculate the friction force that way?

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  • $\begingroup$ You need to define whether there is a horizontal force acting on the box. THe box sitting there, not moving, with no horizontal force acting on it is different than the box sitting there, not moving, with a horizontal force acting on it. $\endgroup$
    – DKNguyen
    Commented Aug 9, 2020 at 4:43
  • $\begingroup$ Is the table flat and horizontal? $\endgroup$
    – my2cts
    Commented Aug 9, 2020 at 8:42

4 Answers 4

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We are told that the box is at rest with respect to the table. So the only frictional force would be static friction. The magnitude of static friction is not the coefficient of friction multiplied by the normal force. The product of the coefficient of static friction and the normal force is equal to the upper limit to the force of friction. The magnitude of the static friction force adjusts itself to whatever value is needed to keep the object at rest with respect to the table.

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  • $\begingroup$ Issue with the second sentence: If there is no horizontal applied force to the box, there is also no friction force. Every sentence after that indicates you understand this well. It is partly the OP's fault for not saying whether a horizontal force is actually being applied to the box or not. All he says is the box is not about to move, which is not enough information. $\endgroup$
    – DKNguyen
    Commented Aug 9, 2020 at 4:41
  • $\begingroup$ @DKNguyen I just copied the exact question....... $\endgroup$
    – CountDOOKU
    Commented Aug 9, 2020 at 5:05
  • $\begingroup$ @DKNguyen Yes. But since the question was silent on the issue, I took the more general assumption that it is possible that there is an applied force. In any event, assuming the possibility of an applied force makes the argument stronger. $\endgroup$
    – garyp
    Commented Aug 9, 2020 at 13:09
  • $\begingroup$ @DKNguyen ... and I also worded the answer to allow for the possibility that the table was in motion. $\endgroup$
    – garyp
    Commented Aug 9, 2020 at 13:22
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If a box is at rest on a level table there is no friction acting on the box. Because if there was friction acting on the box that friction force would be the only horizontal force acting on the box so the box would accelerate and the box doesn't accelerate so there is no horizontal force on the box. Only the weight and the normal force act when the box is at rest.

Imagine the box at rest on level ice there is basically no friction acting on the box.

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Friction force is the force that opposes the relative motion between two surfaces . In your problem since the box sits stationary on the table it means that the two surfaces in contact ( don't take it literally as nothing can be pure contact ) don't slip over each other or their is no relative motion between them.

So there is no friction force between them. If it would have existed the body would have started moving as it's the only external force acting and nothing could have been ever at rest .

So in your case it must be zero from our observations ( if their is no other external force acting on the body) .

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Friction here is static and normal reaction multiply by weight is the maximum friction which can prevent the motion of the block against the external friction , friction can't come into play untill the external force appears that is what Newton third law to produce the friction as reaction you need find a force for action.so what will be the value of friction clearly depend upon the magnitude of force.

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