A question about friction, thanks~

[ThomasJoe40]

Hello, all,

I have got this question which is about friction.

If we pull a cloth, that is covered on a table, with the speed v=3m/s. A cup on the cloth and not far from the edge of the table would not fall off. So, what is the reason for us to give this speed to the cloth?

My opinion (actually a guess) is that a great speed is a result of a great force to cancel out the two frictions from the cup and the table... Am I right? Any suggestions will be warmly welcomed~~~

 

[ceptimus]

The old 'magic trick' of pulling a cloth quickly off a table and leaving the cups and plates still on the table, only works if you pull the cloth real quick.

The reason is that the force imparted on the cup by friction with the cloth is independent of the cloth speed. It doesn't matter if the cloth is going at 5 metres per second relative to the cup, or 100 metres per second - either way the friction force is the same.

For the cup to fall off the table, the force has to be applied to it long enough to accelerate the cup up to a speed that will carry it off the table - the cup could either go over the edge while the cloth is still moving, or it could be going so fast by the time that the cloth has all gone, that friction between the cup and the table is insufficient to stop the cup again before it reaches the edge.

By pulling the cloth really quickly, the cloth isn't in contact with the cup long enough for the friction force to accelerate the cup to the critical speed.

 

[beth314159]

It isn't only the speed that matters

When trying to determine if you are going to be successful in pulling the cloth from under the cup, it is both how large the acceleration of the cloth, and the final speed reached by the cloth. If you gradually increased the speed of the cloth, the cup would follow right along, until both were going 4 m/s, and the cup would cruise right off the end of the table. If you "jerk" the cloth, the cup won't have time to accelerate to a sufficent speed to carry it off the table by the time the cloth is all the way out. Then the cup will slide to the stop on the table. (If the table were frictionless, the cup would achieve some small, but non-zero, velocity during the time you pulled out the cloth, however quickly it occured, and slowly but inevitably drift to the edge of the table, to plummet off.)

-Beth

 

[learningphysics]

I think it's important to point out that static friction is being overcome... If you pulled the cloth slowly (accelerated slowly I mean), the cup would drag along.. here static friction is pulling the cup along with the cloth. But static friction has a limit. It cannot accelerate the cup beyond a certain limit. If you accelerate the cloth super fast, static friction will give way to kinetic friction. This means there is sliding between the cloth and the cup. The cup will still accelerate toward the end of the table but much more slowly than you're pulling the cloth.

 

[ThomasJoe40]

The reason is that the force imparted on the cup by friction with the cloth is independent of the cloth speed...

By pulling the cloth really quickly, the cloth isn't in contact with the cup long enough for the friction force to accelerate the cup to the critical speed...

Thanks. I get what you said. Well, so if...
Impulse (of friction) = mass x velocity 1 - mass x velocity 2
whereas velocity 1 of the cup is zero, so:
Impluse = mass x velocity 2 = constant of friction x g x mass x time of contact
velocity 2 = constant of friction x g x contacting time
So the final velocity of cup will purely depend on the contacting time... right?