Spring & Blocks: Max Friction Force & Oscillation

In summary, the conversation discusses a situation where two blocks, A and B, are connected by a spring and are displaced together and released. The friction between the blocks is a static force that adjusts itself with the applied force. The maximum frictional force at displacement should be less than μmg for the blocks to oscillate without slipping. The conversation also clarifies that the maximum frictional force can never be equal to the maximum displacement, otherwise the blocks wouldn't move at all.
  • #1
zorro
1,384
0
I am stuck up in a situation created by me.

Consider a block A resting on a smooth horizontal surface. There is another block B of the same size/mass resting over it. There is some friction present in between them, with coefficient of friction μ. A spring of spring constant K is attached to block B (the other side attached to a wall off course) and the blocks are displaced through a distance 'x' together and released. The block B oscillates without slipping over the block A.

At the max. displacement, there should be a max. value of the friction force. Now is this value of friction force equal to μmg? If we draw a F.B.D. of block B at max. displacement, we find that Kx should be greater than friction force for the block to oscillate. If the max. value is μmg, and Kx>μmg, then why doesn't the block B slip over the block A?
 
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  • #2
if kx exceeds μmg, there will be slipping and relative motion between the blocks. The frictional force at max displacement has to be less than μmg, only then the blocks will oscillate together without slipping.
Reason: The frictional force is STATIC and not DYNAMIC. Static friction adjusts itself with the amount of force applied on the body. So μmg (where μ is coefficient of static friction) can be a quantity which is greater than Kx (where x is the maximum displacement). If even the extreme value of Kx is less than μmg, then the two bodies never slip against each other.

suppose frictional force is f between the blocks and at maximum displacement,
f(max) = kx (x is maximum at maximum displacement)

f(max) < μmg (for the bodies to never slip)
 
  • #3
androidx219 said:
f(max) = kx (x is maximum at maximum displacement)

If f(max)=kx, how do you think will the block return to its mean position and perform oscillations?
 
  • #4
I am sorry, I was grossly wrong at the statement I made there. Thanks for pointing that out and correcting me. f(max) can never be equal to kx and will always be less than kx, otherwise the blocks wouldn't move at all as you rightly said.

Lets consider the FBDs of A and B separately,

suppose at anypoint say, the combined acceleration is a, then
K.x - f = m.a (for B)
f= m.a (for A)

so k.x = 2m.a

so when considering A and B as a combined body together, f comes out to be a mere inernal force for this system. This should make things a bit clearer to both of us.
 
  • #5


I understand your concern about the situation you have described. In order to answer your question, let's first clarify the concept of friction force and its relationship with the maximum displacement and spring constant.

Friction force is the force that opposes the motion of two surfaces in contact. In this case, it is the force between block B and block A that prevents block B from slipping over block A. The maximum value of friction force can be calculated using the coefficient of friction (μ) and the weight of block B (mg). Therefore, in this scenario, the maximum friction force is indeed equal to μmg.

However, it is important to note that the maximum displacement and spring constant also play a crucial role in determining if block B will slip over block A. The maximum displacement (x) is the distance that the blocks are displaced together before being released. This displacement determines the maximum stretch of the spring and ultimately the maximum force that the spring can exert on block B.

The spring constant (K) is a measure of the stiffness of the spring. A higher spring constant means that the spring will exert a larger force for a given displacement. In your situation, the spring must exert a force greater than the maximum friction force in order for block B to oscillate without slipping.

So, to answer your question, the reason why block B does not slip over block A at the maximum displacement is because the force exerted by the spring (Kx) is greater than the maximum friction force (μmg). As long as Kx is greater than μmg, the block B will continue to oscillate without slipping.

I hope this explanation helps to clarify any confusion you may have had. As a scientist, it is important to consider all factors and variables in a situation to fully understand the phenomenon at hand. Keep exploring and questioning, that's what science is all about!
 

What is the concept of spring and blocks in relation to max friction force and oscillation?

The concept of spring and blocks in this scenario refers to the use of a spring attached to a block to study the effects of friction and oscillation. The block is pulled or pushed by a force, causing it to compress or stretch the spring. The friction between the block and the surface it is placed on determines the maximum force that can be applied to the block before it starts to slide. The oscillation refers to the back and forth motion of the block as it is pulled and released by the spring.

How does the coefficient of friction affect the maximum force that can be applied to the block?

The coefficient of friction is a measure of the force of friction between two surfaces. In this scenario, it determines the maximum force that can be applied to the block before it starts to slide. The higher the coefficient of friction, the greater the maximum force that can be applied to the block without it sliding. This is because a higher coefficient of friction means there is more resistance to the motion of the block, making it more difficult for it to slide.

What is the relationship between the maximum force and the spring constant?

The maximum force applied to the block is directly related to the spring constant. The spring constant is a measure of the stiffness of the spring, and it determines how much force is needed to stretch or compress the spring. A higher spring constant means a stiffer spring, which requires more force to be applied to the block in order to compress or stretch it. Therefore, a higher spring constant will result in a higher maximum force that can be applied to the block.

How does the mass of the block affect the oscillation of the block?

The mass of the block affects the oscillation by changing the rate at which the block moves back and forth. A heavier block will require more force to be moved, resulting in a slower oscillation. On the other hand, a lighter block will require less force and will oscillate at a faster rate. However, the mass of the block does not affect the maximum force that can be applied before it starts to slide.

What factors can affect the accuracy of the results in this experiment?

There are several factors that can affect the accuracy of the results in this experiment. These include the accuracy of the measuring instruments used, the presence of external forces such as air resistance, and the condition of the surfaces in contact with the block. Additionally, human error in conducting the experiment can also affect the accuracy of the results.

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