Kinetic coefficient of friction greater than the static coefficient?

[Manasan3010]

Homework Statement

Are there any instances where kinetic coefficient of friction greater than static coefficient of friction? Is this possible in nature?

Relevant Equations

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Are there any instances where kinetic coefficient of friction greater than static coefficient of friction? Is this possible in nature?

 

[PeroK]

Homework Statement: Are there any instances where kinetic coefficient of friction greater than static coefficient of friction? Is this possible in nature?
Homework Equations: -

Are there any instances where kinetic coefficient of friction greater than static coefficient of friction? Is this possible in nature?

In order to get something moving do you also have to overcome kinetic friction?

 

[Manasan3010]

In order to get something moving do you also have to overcome kinetic friction?

No, we only need to overcome static friction but my question is whether it is possible?
If not are there any theorems or proof that states it is impossible to achieve?

 

[PeroK]

No, we only need to overcome static friction ...

Are you sure about that?

 

[Manasan3010]

Are you sure about that?

Net force in a particular direction should be higher than maximum static friction between the surfaces for motion to take place in that particular direction. I am more confused than before.

From Live Science

Friction also acts in stationary objects. Static friction prevents objects from moving and is generally higher than the frictional force experienced by the same two objects when they are moving relative to each other. Static friction is what keeps a box on an incline from sliding to the bottom.

 

[PeroK]

Net force in a particular direction should be higher than maximum static friction between the surfaces for motion to take place in that particular direction. I am more confused than before.

From Live Science

You could ask over what distance static friction applies? And what is the kinetic energy of the object when kinetic friction takes over?

 

[Manasan3010]

You could ask over what distance static friction applies?

Static Friction applies in a non-moving body so distance applied is 0

And what is the kinetic energy of the object when kinetic friction takes over?

The moment kinetic fraction takes over, object's velocity will be 0 and acceleration will be a non zero integer SO the kinetic energy will be 0 . After that moment velocity will increase linearly so kinetic energy will increase quadratically.

 

[PeroK]

Static Friction applies in a non-moving body so distance applied is 0The moment kinetic fraction takes over, object's velocity will be 0 and acceleration will be a non zero integer SO the kinetic energy will be 0 . After that moment velocity will increase linearly so kinetic energy will increase quadratically.

What if the applied force is greater than the static friction but less than the kinetic friction?

 

[Manasan3010]

What if the applied force is greater than the static friction but less than the kinetic friction?

I think the object will start to move with an acceleration and after that the kinetic frictional force will balance the applied force and object will have 0 acceleration and no change in previous motion and will continue to move with constant velocity.

 

[kuruman]

Here is a thought experiment inspired by post #2 by @PeroK. Put a block of mass $m$ on a horizontal piece of plywood. Lift one edge of the plywood veeery slowly to create an increasing angle $\theta$ with the horizontal. There will be a critical angle $\theta_c$ at which the force of static friction reaches its maximum value $f_s^{max}=\mu_s~N=\mu_s~mg\cos\theta_c$. The component of gravity down the incline is $F_x=mg\sin\theta_c$. Setting the two equal just before the block starts sliding, gives the condition,$$\mu_s mg \cos\theta_c=mg \sin\theta_c.$$ At that point the block is not sliding yet. Now increase the angle by a very small amount $\delta\theta$ beyond $\theta_c$. The maximum static friction, $f_x^{max}$ remains the same. The component of gravity along the incline becomes, to first order, $$F_x=mg\sin(\theta_c+\delta\theta)\approx mg(\sin\theta_c+\delta\theta)=\mu_s mg \cos\theta_c+mg(\delta\theta)=f_s^{max}+mg(\delta\theta)$$ At this point the block starts sliding because, clearly, $F_x>f_s^{max}$. At this point the normal force is, to first order, unchanged,$$N=mg\cos(\theta_c+\delta\theta)\approx mg\cos\theta_c.$$Because the block is now sliding, the force of friction opposing gravity is $$f_k=\mu_kN=\mu_k mg\cos\theta_c.$$For the block to keep on sliding, $$f_k \leq F_x \rightarrow~\mu_k mg\cos\theta_c \leq \mu_s mg \cos\theta_c+mg(\delta\theta) $$which results in$$(\mu_k -\mu_s)\cos\theta_c \leq \delta\theta .$$The inequality is certainly satisfied if $\mu_k <\mu_s$ because $\delta\theta$ is positive. If $\mu_k >\mu_s$ note that $\delta\theta$ can be made arbitrarily small and in the limit $\delta\theta \rightarrow 0$, $\mu_k =\mu_s$. When you have equality, it means that the block slides with constant velocity right at the critical angle for the maximum value of static friction and I see no reason why that cannot be so. However, as you can see by the very definition of these coefficients of friction, it must be that $$\mu_k \leq \mu_s.$$

 

[PeroK]

I think the object will start to move with an acceleration and after that the kinetic frictional force will balance the applied force and object will have 0 acceleration and no change in previous motion and will continue to move with constant velocity.

If kinetic friction is greater than the applied force then the object will slow down, surely? How can an object keep moving at constant velocity if there is a net regarding force?

 

[Manasan3010]

If kinetic friction is greater than the applied force then the object will slow down, surely? How can an object keep moving at constant velocity if there is a net regarding force?

Isn't it maximum kinetic fraction So It will oppose the opposite force by matching its value like in static friction OR is it different for kinetic friction?

 

[kuruman]

Isn't it maximum kinetic fraction So It will oppose the opposite force by matching its value like in static friction OR is it different for kinetic friction?

It's different. There is no maximum kinetic friction and according to the simplified model the kinetic friction is constant and given by $f_k=\mu_k N$ In real life kinetic friction is velocity-dependent and goes to zero when the velocity goes to zero,

 

[PeroK]

Isn't it maximum kinetic fraction So It will oppose the opposite force by matching its value like in static friction OR is it different for kinetic friction?

Hmm. Static friction matches the applied force because if you got the maximum static friction, the object would move in the opposite direction to the applied force!

As @kuruman says kinetic friction is always at a maximum. Otherwise, if there were no applied force, there would be no kinetic friction. Kinetic friction acts on a body in motion, regardless of whether the body is subject to any other forces.