A very very interesting question of friction!!?

Question

Well I have read that friction always opposes the motion between bodies. But here is a situation where friction really have to decide what to do...
Consider a block lying on a frictionless table..
Now another block is kept on it. But there is some friction between the the blocks.
Ok, now If I pull the lower block the friction offered by the top block will oppose it and by NEWTONS THIRD LAW the bottom block will also push the top block in the direction of MOTION.

NOW MY QUESTION::
If I pull the lower block with a force less than limiting friction( that offered by top block) it will certainly not move.
BUT, newtons third law says the same friction acts on top one by bottom! So WILL THE TOP BLOCK MOVE??? What will happen after that, will friction change direction ???

Answer 1

I think the problem is with the "limiting value" of friction. I assume you mean you'll be pulling with a force below that which would cause the blocks to slide relative to each other (I can't think of anything else "limiting value" would mean). So, the force of friction between the two blocks is the force of *static* friction.



Remember that the force of static friction is self-adjusting. So it's zero before you start to pull on the bottom block. As you pull on the bottom block, it will increase, but it won't increase enough to prevent the bottom block from moving--it will only increase enough to keep the top block from sliding. This statement isn't true:



"If I pull the lower block with a force less than limiting friction( that offered by top block) it will certainly not move."



If the bottom block is on a frictionless surface, there is no force you could pull with that is small enough for the bottom block not to move.

Answer 2

It is unclear what you are suggesting... (and unclear if you understand what you are suggesting).



Do a Free Body Diagram. Since one block is on a frictionless table, the only forces will be gravity and the friction with the second block. You need to look at the "reaction" due to inertia as the bottom block accelerates for velocity zero to some constant velocity (or maybe you plan to have the acceleration constant???).

Answer 3

Your logic is flawed. If the force is less than what's needed to overcome friction, there is no movement between the blocks. This doesn't violate Newton's Third. Friction will not "change direction" spontaneously.

Answer 4

no the blocks will move with same acceleration/velocity

IF friction btwn ground is zero



the ans lies in your question itself

friction opposes motion NOT any motion but RELATIVE motion

since you are pushing the lower block

if it does not move the upper one will move

which gives it relative velocity which friction will try to minimize



so both blocks will move with same velocity in direction of force

on the lower block friction is backwards(opposite to force)

on the upper block it is in the same direction as the force