Solving Friction Problem: Box on Ground, Force Applied

[terence1732]

As follows,
a box is placed on the ground
And let the limiting static friction be 5N
for instance an external force 2N is applied to the box
Then, will the friction on the box be 2N?
if yes, then .. there will be a friction of 2N on the earth? causes they are action and rxn pair
And will the Earth move but the box will not move?

or will the box and the Earth just share the 2N force and move together? the friction between them is not exactly 2N but much smaller then it?
But, in this way, a much greater applied force (>5N) will be needed to cause relative movement

I just can't find out what i am missing.
Pls help thanks a lot

 

[Doc Al]

As follows,
a box is placed on the ground
And let the limiting static friction be 5N
for instance an external force 2N is applied to the box
Then, will the friction on the box be 2N?

Yes.

if yes, then .. there will be a friction of 2N on the earth? causes they are action and rxn pair

Yes.

And will the Earth move but the box will not move?

or will the box and the Earth just share the 2N force and move together? the friction between them is not exactly 2N but much smaller then it?

Whether the Earth accelerates or not depends on the net force. If the 2N force is external to the earth, then box and Earth will move together. Note that the acceleration will be miniscule, but it implies that the friction force on the box will be slightly less than 2N. (Newton's 2nd law.)

But, in this way, a much greater applied force (>5N) will be needed to cause relative movement

No, just a tiny bit greater than 5N. (Way too small to ever measure or notice! This is just a theoretical point.)

 

[terence1732]

Thank for your help
But now I hv another problem..
A case as follows,
Now I place a box (1kg) on the ground.
Assume there's no friction between the ground and this box.

And I place another box (also 1 kg) above this box
The limiting static friction between this two box is 5N

And now external force of 2N is applied to the lower box
Will they move together?
If yes, then the friction between the box surface should be 1N?

And I want to cause a relative movement between boxes,
should the external force be greater then 10N?

It seems that it is quite strange..

 

[Doc Al]

And now external force of 2N is applied to the lower box
Will they move together?
If yes, then the friction between the box surface should be 1N?

Right. The surfaces will resist slipping until they reach the static friction limit. In this case only 1 N of friction is required, which is well within the limit.

And I want to cause a relative movement between boxes,
should the external force be greater then 10N?

Right. You need to create a situation where more force is required to accelerate the block than static friction can provide. In this case, that means an acceleration of 5 m/s^2, which requires a force of 10 N. (Once the upper block begins to slip, less force will be required to maintain slipping since static friction will be replaced by kinetic friction.)

It seems that it is quite strange..

Strange but true.