Two block problems with friction

In summary: Consider this: Suppose blocks are made of metal and the maximum static friction coefficient between the blocks is 1.0. If the force on block A is increased from 30N to 40N, the block will start to slide across the block B. The force on block B is now greater than the force on block A, so the block B will start to slide. I can't make any sense of that. Something has to happen!
  • #1
Hamiltonian
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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.
 
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  • #2
Hamiltonian299792458 said:
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).
 
  • #3
PeroK said:
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?
 
  • #4
Hamiltonian299792458 said:
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.
 
  • #5
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?
 
  • #6
gleem said:
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.
 
  • #7
Hamiltonian299792458 said:
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.
 
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Related to Two block problems with friction

1. What is a two block problem with friction?

A two block problem with friction is a physics problem that involves two blocks of different masses connected by a rope or string, with one block resting on a surface with friction. The goal is to determine the acceleration and tension in the rope or string.

2. How do you solve a two block problem with friction?

To solve a two block problem with friction, you must first draw a free body diagram for each block, labeling all the forces acting on them. Then, use Newton's second law (F=ma) to write equations for the forces in the x and y directions. Finally, solve the equations simultaneously to find the acceleration and tension.

3. What is the role of friction in a two block problem?

Friction plays a crucial role in a two block problem because it is the force that opposes the motion of the block on the surface. This means that it will affect the acceleration and tension in the rope or string connecting the two blocks.

4. How does the coefficient of friction affect a two block problem?

The coefficient of friction is a measure of how rough or smooth the surface is. It affects a two block problem by determining the strength of the frictional force acting on the block. A higher coefficient of friction means a stronger frictional force, which will result in a lower acceleration and higher tension in the rope or string.

5. What are some common misconceptions about two block problems with friction?

One common misconception is that the frictional force is always equal to the weight of the block. In reality, the frictional force can vary depending on the coefficient of friction and the other forces acting on the block. Another misconception is that the acceleration and tension will always be the same for both blocks, when in fact they can be different due to the different masses of the blocks.

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