Newton 2nd law + frame of reference

[fisico30]

hello forum,

i am struggling with the conceptual understanding of this problem:
Given two blocks, one on top of the other. There is friction between the two blocks.
The upper block is pulled with a force F. Thanks to friction, as long as F is smaller or equal to the static friction f_s(max) the objects will move, accelerate together, withouth having the top block slide over the lower block...

The free-body diagram of the top block involves only two forces in the horizontal direction: F and f_s. F=f_s for the top block not to slide while being pulled.

But that seems from the frame of reference of the lower block...

If we are observing the situation from the ground, the top (and bottom) block is accelerating, moving, so a net force need to be there...

The upper block is not moving relative to the lower block (relative velocity=0).

What is the correct frame of reference to use? I would say the one fixed with the ground (because inertial). But that would imply a net force on the top block, while we just have

F=f_s

thanks
fisico30

 

[Doc Al]

The free-body diagram of the top block involves only two forces in the horizontal direction: F and f_s.

That's true.

F=f_s for the top block not to slide while being pulled.

That's not true.

But that seems from the frame of reference of the lower block...

If we are observing the situation from the ground, the top (and bottom) block is accelerating, moving, so a net force need to be there...

Absolutely.

The upper block is not moving relative to the lower block (relative velocity=0).

What is the correct frame of reference to use? I would say the one fixed with the ground (because inertial). But that would imply a net force on the top block, while we just have

F=f_s

You can use either frame to analyze this problem. To use the inertial frame of the ground, just apply Newton's 2nd law as usual to both blocks.

But if you want to use the accelerating frame of the bottom block, then you'll have to modify Newton's laws to include an inertial force acting on the top block. The sum of all forces--including the inertial force--must add to zero. That's a bit different from saying F = f_s (which isn't true).