Pretty Quick Question - Circular Motion

[sippadi]

Homework Statement

A 0.50-kg ball, attached to the end of a horizontal cord, is rotated in a circle on a frictionless horizontal surface. The chord will break if the tension exceeds 50N, so there is a maximum velocity for the ball. However, if there was friction on the surface, would the maximum velocity be affected?

Homework Equations

Fn (u) = Ff

The Attempt at a Solution

I think if there was friction, the friction would pull the ball in more, thus lessening the tension in the string which increases the maximum velocity. However, wouldn't there be tangential friction as well?

 

[kuruman]

Hi sippadi, welcome to PF.

Yes, there is tangential friction and it will reduce the speed. However, if the maximum tension of 50N is to be affected by friction, friction must have a radial component. What must be true to have a radial component of friction?

 

[sippadi]

The bottom of the ball must be at rest with the surface, in order for static friction to exist, which is the cause of the radial component of friction. Or the surface has to move with respect to the ball.. I think.

I've already asked two teachers this; one thinks only tangential friction exists and the other thinks both exists.

 

[sippadi]

My physics teacher actually posted the answer; the friction would have no effect as the opposition is perpendicular to the cord tension. I don't get it.. Can anyone please help?

Thanks a lot :)

 

[kuruman]

You have to understand how tension actually works. Suppose the surface is frictionless to begin with. As the mass goes around the circle, the higher the speed the more tension is needed to keep it in the circle. How does the cord "know" how much tension is needed? It stretches a little bit (like a stiff spring) and this increases the tension. If there is friction, it will prevent this stretching from happening at first. In other words, static friction assists tension so that the speed of the mass around the circle before the cord breaks will be higher than the case without friction.

Your teacher is thinking of kinetic friction that is always opposite to the velocity, i.e. perpendicular to the tension. To add to or subtract from the tension, you need a component of friction along the cord which is definitely not kinetic friction but could be static friction.

This problem has additional complications although I am not sure your teacher wanted you to go there. What I said above applies to a block sliding on the surface. If we have a ball going around with friction as the problem states, then the ball will have to roll as it goes around the center of the circle. In that case there is orbital angular momentum about the center of the circle and rolling angular momentum about the instantaneous point of contact. It suffices to say that the rolling angular momentum is continuously changing direction and for that to happen a torque is needed. This torque is provided by the tension. So, yes, things are different when one considers friction.

 

[sippadi]

Thanks so much for your help :) Do you mind answering one more quick question?

Are you sure static friction exists? My friends think that only kinetic friction will apply (which doesn't affect the maximum velocity).

Here's a response I read somewhere else:
"This may not be a very informative answer, but here's my opinion. I guess you're thinking of this situation similarly to a vehicle making a turn on a curved road, whereby static friction between the tires and road kicks in. But static friction only applies on tires because the tires do not slide on the road, they spin. This means that for a split, very small fraction of a second, the contact point between the tires and the road experiences a static frictional force. However, from my understanding in your situation, the ball is sliding. This means that static friction cannot be considered, and you can only apply kinetic friction."

if there's kinetic friction ONLY, then there's no affect on the velocity. According to him, only kinetic friction exists.

I hope this doesn't trouble you too much. Again, thanks a lot

 

[sippadi]

I understand now.. nvm