# What are the rules for static and kinetic friction?

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• terryds
In summary, when a bottle is placed on a sheet of paper at the edge of a table and the sheet is pulled slowly, the bottle remains on the table due to the static frictional force between the bottle and the paper. However, when the paper is pulled quickly, the frictional force becomes kinetic and the bottle slides off the table due to the lower coefficient of kinetic friction. This is because the acceleration of the bottle becomes very small. This is also known as inertial resistance, which is simply the reaction force of the bottle on the paper. Additionally, kinetic friction between two surfaces always points in the opposite direction of the velocity of one surface relative to the other.
terryds
A bottle is placed on a sheet of paper at the edge of a table. The sheet is pulled slowly at first but very quickly when it has reached the very end of the edge. The bottle remains on the table.
Why does this happen?

I think what happens in the initial condition (when it's still pulled slowly) is that there is static frictional force between bottle and the paper which makes the bottle goes the same way as the paper.
But, when the paper is pulled very quickly, the frictional force becomes kinetic frictional force. Since the coefficient of kinetic friction is much less than the static one, the acceleration of the bottle becomes very very small so the bottle doesn't fall off the table.

But, after googling (https://www.quora.com/What-is-the-principle-behind-the-table-cloth-trick), I found out that it's due to the inertial resistance. What is actually inertial resistance? Is it a force or a vector? What's the formula? I really don't get it.

The reference that you provide is confusing in my opinion. I understand mass and acceleration but not inertial resistance. Remember, static friction has an upper limit that it cannot exceed. When you start pulling on the paper slowly, your action accelerates the paper with some acceleration a regardless of how hard you pull. When you pull gently, the acceleration is small so that an object of mass m placed on the paper is accelerated by static friction and moves with it without sliding with the same acceleration as the paper. This is because ma is less than the upper limit of the force of static friction. When you pull rapidly, ma exceeds the maximum force of static friction almost immediately and the object slides relative to the paper.

terryds
kuruman said:
The reference that you provide is confusing in my opinion. I understand mass and acceleration but not inertial resistance. Remember, static friction has an upper limit that it cannot exceed. When you start pulling on the paper slowly, your action accelerates the paper with some acceleration a regardless of how hard you pull. When you pull gently, the acceleration is small so that an object of mass m placed on the paper is accelerated by static friction and moves with it without sliding with the same acceleration as the paper. This is because ma is less than the upper limit of the force of static friction. When you pull rapidly, ma exceeds the maximum force of static friction almost immediately and the object slides relative to the paper.

Another question :

1. Does the friction between the bottle and the paper has a reaction conjugate? I mean, if there is action (in this case: friction), is there any reaction??
For example, the static friction between bottle and paper has the same direction as the direction I pull the paper, so there is reaction force which exerts on the paper caused by the ball, right? (as a reaction of static frictional force)

2. Does the kinetic friction has the same direction as the direction I pull the paper?? I doubt it since the bottle remains on the table when yanked quickly. So, does the direction of friction force change (become the opposite) as it goes from static to kinetic in this case? Or, does the direction remain the same, but the acceleration is just so slow?

Good questions.

1. According to Newton's Third Law, every action has a reaction. The paper pushes the bottle forward and the bottle exerts a backward force on the paper. You accelerate the paper not the bottle, you are not even touching the bottle. It is the forward force of static friction exerted by the paper that accelerates the bottle. Of course, the paper cannot accelerate the bottle all by itself, that's why you might think that it is the force from your hand that does it. Your hand accelerates the paper not the bottle. Now, your hand that pulls the paper feels (through the paper) the backward reaction force that the bottle exerts on the paper. It's that backward reaction force that your reference calls "inertial resistance", an unfortunate name.

2. Don't forget that when you pull the paper forward very rapidly, the bottle is at rest relative to the table but slides relative to the paper. Kinetic friction on an object is always opposite to the velocity of the object. Since the paper slides forward, the kinetic friction on it will be backward. Therefore the kinetic friction on the bottle will be forward. It's the same situation as if you held the bottle with your hand and slid the paper under it.

Here are two simple rules for static and kinetic friction:

Static friction adjusts itself in magnitude and direction to provide the observed acceleration, but only up to a certain limit that it cannot exceed.
Kinetic friction only exists between two surfaces that are rubbing as they move past each other and points in the opposite direction of the velocity of one surface relative to the other.

## 1. How does the tablecloth trick work?

The tablecloth trick is based on the principle of inertia. The objects on the table have a tendency to resist any change in their state of motion. When the tablecloth is pulled quickly, the objects on top of it (such as plates, glasses, and cutlery) will remain in their original state of rest due to inertia, while the friction between the tablecloth and the objects is not strong enough to overcome this inertia. This creates the illusion that the objects are magically staying in place while the tablecloth is being removed.

## 2. Is there a certain type of tablecloth that works best for this trick?

The tablecloth material does not play a significant role in the success of the trick. However, a smooth and slippery material (such as silk or satin) will reduce friction and make it easier to pull the tablecloth quickly without disturbing the objects on the table.

## 3. Can this trick be done with any type of tableware?

Yes, the trick can be done with any type of tableware as long as the objects are placed close enough together on the table, and there is enough room for the tablecloth to be pulled without knocking anything over. It is important to note that fragile objects (such as glassware) should be handled with care to avoid any accidents.

## 4. Do I need any special skills to perform the tablecloth trick?

The tablecloth trick can be performed by anyone with some practice and coordination. It is important to pull the tablecloth quickly and smoothly, without jerking or tugging, to ensure that the objects stay in place. It may take a few attempts to get the timing and technique right, but with some practice, anyone can successfully perform this trick.

## 5. Are there any safety precautions I should take while performing the tablecloth trick?

Yes, it is important to take some safety precautions while performing the tablecloth trick. Make sure to remove any sharp or fragile objects from the table before attempting the trick. Also, avoid using a heavy or large tablecloth that may cause the table to tip over when pulled. It is always better to practice with a smaller tablecloth and gradually increase the size as you become more comfortable with the trick.

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