# B Static friction vs kinetic friction in Tablecloth trick

1. Oct 7, 2016

### terryds

In the tablecloth trick, if we pull the tablecloth with a great force, the objects on it will stay on the table. But, if we pull it gently, the objects on it will still get along with the cloth movement.

I know that if the force exceeds the maximum value of static friction, the objects will stay on the table.
But, I still don't understand two things.

1. What static friction should be exceeded to do the trick? Is it the table-cloth or objects-cloth friction? At first, I think it is objects-cloth friction since it's those objects that's affected. But, the force exerting on objects are just the friction force since we apply the force only to the cloth not the objects, right? If the only force exerting on objects are friction, I don't understand which force that the friction affects. I mean, in order to know the objects will move or not, we should know two forces (the friction and the force), right?

2. The objects stay on the table because it can't 'catch' the cloth, right? (objects move very slowly so it can't 'catch' the cloth) or, does the kinetic friction makes the objects move in opposite direction of the cloth??

2. Oct 7, 2016

### BvU

Hi,
1. object-cloth static friction has to be exceeded to accelerate the objects.

If you pull gently, you have to overcome the cloth-table friction; the remainder of the force is then used to accelerate the objects (A little)

2. Right, in the sense that the objects can't accelerate as fast as the cloth. They can move at considerable speed, but that's not releant here. It's about acceleration.

And they will never move in a direction opposite to that of the cloth: there simply is no net force in that direction to be found anywhere in the situation.

The trick works so nicely because generally the kinetic friction is less than the static friction

3. Oct 7, 2016

### drvrm

When one pulls the table cloth - at the cloth and objects surface interface a force is exerted by the object which resists its motion -as the pulling-force is increased the frictional force may come to the limiting situation and the pulling force carries the body (there is no relative motion between the surfaces in contact) with uniform speed changing the inertial state of the glass. this happens when the pulling force is slowly raised and frictional force builds up.
here the coefficient of static friction multiplied by the normal reaction is the limit.
The Force of friction always opposes the tendency of relative motion and its a self adjusting force.
on the other hand if you give a jerk/impulsive force and its much larger than limiting frictional force the relative motion between the two surfaces leads to kinetic friction which is less than the static friction .The body's lower surface exerts an opposing force and the cloth's surface acts to carry the body in the direction of the pull
the cloth can not carry it and the body can not tag itself to the cloth and remains as it is .

4. Oct 7, 2016

### terryds

So, the pulling force which is exerted on the cloth must exceed the maximum static friction of objects-cloth?
So, it is
F - F max static (object-cloth) - F kinetic (cloth-table) = (mass of cloth+objects) * a

And, then we substitute a = maximum static friction / object mass

Correct?

5. Oct 7, 2016

### BvU

The idea is that the objects are accelerated only minimally, so (preferably a lot) less than maximum static friction / object mass
And the cloth should accelerate rapidly.

6. Oct 7, 2016

### CWatters

Draw a free body diagram for an object. Work out the net force and acceleration. Objects will move as neither static friction or kenetic is zero (so there is always a net force when the cloth is moving). The object stays on the table if it doesn't move far enough to fall off. The distance it moves depends on how long the force acts and how far the object is from the edge. The duration of the applied force depends on the dimensions of the cloth and how fast it moves past the object. In principle you can apply the equations of motion to work out how far objects will move.

If static friction isn't exceeded objects move with the cloth so will fall off if the cloth is moved far enough.

7. Oct 7, 2016

### Khashishi

It's important to move the cloth quickly, to minimize the time over which the cloth exerts force on the cups (through kinetic friction).