Two block problems with friction

[Hamiltonian]

Homework Statement

A block of mass 20kg is placed on another block of 10kg the coefficient of static friction between the two surfaces = 0.3
the surface of contact between the 10kg block and floor is smooth. A force of 30N acts on the 20kg block. comment on the motion of the system

Relevant Equations

F = ma

the maximum value of friction between the surfaces of the blocks is $60N$
the friction should be self-adjusting until this maximum value. Hence the force of friction in the given scenario should be = 30N but this is physically impossible as if this is the case the top block will be at rest and the bottom block will move.
hence I made the equations $$30 - f = 20a $$ $$10a = f$$

from this I got $f = 10N$
but I don't understand why we are supposed to form these two equations are we supposed to do this out of necessity as we cannot say friction will be self-adjusting in the given scenario as it will lead to a physically impossible situation?
I don't as such have an issue with the question rather I don't understand why the above equations yield a correct answer as here friction is not-self adjusting.

 

[PeroK]

Homework Statement:: A block of mass 20kg is placed on another block of 10kg the coefficient of static friction between the two surfaces = 0.3
the surface of contact between the 10kg block and floor is smooth. A force of 30N acts on the 20kg block. comment on the motion of the system
Relevant Equations:: F = ma

the maximum value of friction between the surfaces of the blocks is $60N$
the friction should be self-adjusting until this maximum value. Hence the force of friction in the given scenario should be = 30N but this is physically impossible as if this is the case the top block will be at rest and the bottom block will move.
hence I made the equations $$30 - f = 20a $$ $$10a = f$$

from this I got $f = 10N$
but I don't understand why we are supposed to form these two equations are we supposed to do this out of necessity as we cannot say friction will be self-adjusting in the given scenario as it will lead to a physically impossible situation?
I don't as such have an issue with the question rather I don't understand why the above equations yield a correct answer as here friction is not-self adjusting.

The answer you found is the only answer that makes physical sense. There are only two physically viable options:

a) Both block accelerate together. This requires sufficient friction between the blocks.

b) The top block has a greater acceleration and slides across the bottom block. This requires insufficient friction for option a).

 

[Hamiltonian]

The answer you found is the only answer that makes physical sense. There are only two physically viable options:

a) Both block accelerate together.

b) The top block has a greater acceleration and slides across the bottom block.

are we supposed to do this out of necessity as we cannot say friction will be self-adjusting in the given scenario as it will lead to a physically impossible situation?

 

[PeroK]

are we supposed to do this out of necessity as we cannot say friction will be self-adjusting in the given scenario as it will lead to a physically impossible situation?

I can't make any sense of that. Something has to happen!

If you don't like the physical solution you found, then propose another one.

 

[gleem]

Consider this, it is the force of friction that is responsible for the acceleration of the 10 Kg block. That force is constant as the 20 Kg block slides across it. What do you expect if the force on the 20 Kg block is increased or the coefficient of friction is decreased?

 

[Hamiltonian]

Consider this, it is the force of friction that is responsible for the acceleration of the 10 Kg block. That force is constant as the 20 Kg block slides across it. What do you expect if the force on the 20 Kg block is increased or the coefficient of friction is decreased?

it is indeed the force of friction that is responsible for the acceleration of the 10kg block.
the coefficient of friction has to be constant for a pair of surfaces!

p.s. I am having difficulty explaining my question (which I know is a bad sign) hence I think it would be best not to spend more time on this if I am able to rephrase my question in a better way I will post it.

 

[haruspex]

the friction should be self-adjusting until this maximum value. Hence the force of friction in the given scenario should be = 30N

Self-adjusting, yes, but to what criterion? Friction relates to relative tangential motion of the surfaces in contact. In static friction, the force adjusts, if it can, to ensure no relative motion. There is no reason to suppose that requires 30N.