Tablecloth Trick: Explaining Newton's Laws

[Skrphys]

I have my students doing a lab where they have to do and explain the tablecloth trick using Newton’s Laws. The problem I am having is that the one question asks why the quick removal of the tablecloth matters. I know friction is not affected by speed and yet this is the only force acting on the plate/cup in the direction of acceleration. So if speed doesn’t affect friction why can the trick not be done slowly? I have racked my brain thinking about it and I just can’t seem to come up with a good explanation. Any ideas on why this works this way? I know inertia makes the plate/cup “want” to stay at rest but that doesn’t explain why the friction doesn’t always cause the objects to fall.

 

[A.T.]

I have my students doing a lab where they have to do and explain the tablecloth trick using Newton’s Laws. The problem I am having is that the one question asks why the quick removal of the tablecloth matters. I know friction is not affected by speed and yet this is the only force acting on the plate/cup in the direction of acceleration. So if speed doesn’t affect friction why can the trick not be done slowly? I have racked my brain thinking about it and I just can’t seem to come up with a good explanation. Any ideas on why this works this way? I know inertia makes the plate/cup “want” to stay at rest but that doesn’t explain why the friction doesn’t always cause the objects to fall.

1) If the acceleration is too low, static friction will never break.

2) The longer kinetic friction acts, the more horizontal momentum is transferred.

 

[sophiecentaur]

There is a quantity called Impulse, which is the relevant factor here. Impulse is Force X time and Impulse is equal to the change in momentum of the object it's applied to.
When you whip away the table cloth, the friction force pulling the plate will be much the same, once the cloth is actually slipping, whatever the speed of the cloth is. The quicker you pull the cloth, the shorter the time and so the less the Impulse is. So the mass X velocity (momentum) of the plate will be less in the end. Once the cloth has gone, the plate may be sliding a bit on the table but it will soon slow down.
If you fail to pull fast enough, the plate will not slip and it will be pulled over the edge. Ripples and ridges in the cloth can upset the trick by increasing the sideways force.

 

[Skrphys]

There is a quantity called Impulse, which is the relevant factor here. Impulse is Force X time and Impulse is equal to the change in momentum of the object it's applied to.
When you whip away the table cloth, the friction force pulling the plate will be much the same, once the cloth is actually slipping, whatever the speed of the cloth is. The quicker you pull the cloth, the shorter the time and so the less the Impulse is. So the mass X velocity (momentum) of the plate will be less in the end. Once the cloth has gone, the plate may be sliding a bit on the table but it will soon slow down.
If you fail to pull fast enough, the plate will not slip and it will be pulled over the edge. Ripples and ridges in the cloth can upset the trick by increasing the sideways force.

Awesome! This is how I was trying to explain it too but my explanation got lost after the definition of impulse. I was having trouble connecting it to the speed. So I’m the end, and correct me if I’m wrong, it’s because acceleration is dependent on time so we can still say f=ma applies because acceleration is dependent on time. So a longer time of acceleration still gives the same force.

 

[sophiecentaur]

Awesome! This is how I was trying to explain it too but my explanation got lost after the definition of impulse. I was having trouble connecting it to the speed. So I’m the end, and correct me if I’m wrong, it’s because acceleration is dependent on time so we can still say f=ma applies because acceleration is dependent on time. So a longer time of acceleration still gives the same force.

The acceleration is a bit secondary in this. What counts is making sure that the Impulse is small, by keeping the contact time short. If the final speed of the plate is low enough you can say that the acceleration is almost zero. It is very counter intuitive that the faster you pull the cloth, the less the plate is affected. That assumes that the coefficient of kinetic friction is independent of tangential speed but high speed contact can even reduce the friction force in some cases, just beyond the slipping condition.
Impulse is often not stressed enough at School level. I don't remember anyone bringing it in during my early A Level Dynamics course but it is really good for solving many problems. PF gets many questions about "The force of the collision" between two objects, when it can often be totally ignored in many problems.

 

[A.T.]

it’s because acceleration is dependent on time so we can still say f=ma applies because acceleration is dependent on time. So a longer time of acceleration still gives the same force.

Acceleration is relevant in the initial phase, to start the sliding (overcome static friction). Velocity is relevant during the sliding, to minimize the duration of force application (impulse or transferred momentum). Obviously, the more acceleration throughout, the higher the average velocity, so acceleration is relevant for minimizing the impulse as well.

 

[Skrphys]

The acceleration is a bit secondary in this. What counts is making sure that the Impulse is small, by keeping the contact time short. If the final speed of the plate is low enough you can say that the acceleration is almost zero. It is very counter intuitive that the faster you pull the cloth, the less the plate is affected. That assumes that the coefficient of kinetic friction is independent of tangential speed but high speed contact can even reduce the friction force in some cases, just beyond the slipping condition.
Impulse is often not stressed enough at School level. I don't remember anyone bringing it in during my early A Level Dynamics course but it is really good for solving many problems. PF gets many questions about "The force of the collision" between two objects, when it can often be totally ignored in many problems.

Thanks for your reply. Maybe my conceptual understanding of impulse is lacking. You are right, it definitely isn’t talked enough about. Even in college I only recall briefly discussing it.

 

[sophiecentaur]

Acceleration is relevant in the initial phase, to start the sliding (overcome static friction). Velocity is relevant during the sliding, to minimize the duration of force application (impulse or transferred momentum).

The relevant acceleration is of the cloth and it needs to be great enough to make the force greater than the static friction. The acceleration of the plate is as low as you can manage to get it. This problem is one sage harder than your average SUVAT style question. I guess it's an early introduction to non linear forces.

 

[A.T.]

Thanks for your reply. Maybe my conceptual understanding of impulse is lacking. You are right, it definitely isn’t talked enough about. Even in college I only recall briefly discussing it.

You must have heard of momentum. Impulse is just a fancy name for momentum transferred via a force:

https://en.wikipedia.org/wiki/Momentum#Relation_to_force

 

[sophiecentaur]

Maybe my conceptual understanding of impulse is lacking.

Not really. It is probably more a matter of familiarity than understanding. It's almost too good to be true that you can ignore the details of the motion and just look at the Momentum before and after the event. We did the billiard ball problems and ignored the actual event of collision by talking of Coefficient of Restitution. A bit of sleight of hand there for the sake of the student, I think and we accepted it rather than looking too closely at our assumption. Quick and dirty often works.

 

[sophiecentaur]

You must have heard of momentum. Impulse is just a fancy name for momentum transferred via a force:

https://en.wikipedia.org/wiki/Momentum#Relation_to_force

I would call it 'shorthand', rather than "fancy". It is an elegant way to package a description of something that does away with needing to know which force and for how long. it acknowledges that the nuts and bolts of the interaction need not be considered. It wasn't taught to me and, when I heard it used, many years later, it was immediately an attractive concept.