Vertical circular motion help

[kplooksafterme]

[SOLVED] Vertical circular motion help!

Homework Statement

A 17.4 g steel marble is spun so that it rolls at 171.0 rpm around the inside of a vertically oriented steel tube. The tube, shown below, is 13.0 cm in diameter. Assume that the rolling resistance is small enough for the marble to maintain 171.0 rpm for several seconds. What is the force of static friction required for the marble to not spiral down the inside of the tube? (For steel on steel μK=0.600 and μS=0.800.)

Homework Equations

The Attempt at a Solution

I figured the vertical component of static friction must be equal to the weight of the object. The normal force on the centripetal axis can be found from the angular velocity, that is, F(n) = m x (angular velocity)^2 x r. Then I calculated the kinetic friction force on the tangential axis using this normal force, F(kinetic friction) = 0.6 x N. Finally, because the ball moves with a constant angular velocity for a few seconds I figured the magnitude of the tangential static friction force muse be equal to the magnitude of the tangential kinetic friction force. I summed the two static friction forces using Pythagorean theorem, but didn't get the correct answer.
I have correctly converted units, etc. I just need to know if my approach is sound? Thanks in advance for any help

 

[Dick]

Kinetic frictional force and static frictional force don't operate at the same time. For rolling motion you want only the static.

 

[kplooksafterme]

So how would I calculate the tangential static friction force in this situation? Wouldn't I need to know whatever other tangential force is causing the ball not to accelerate tangentially?

 

[Dick]

I don't think so. You are told that the 'rolling resistance' is small enough that the ball maintains it's speed for several seconds. I think this is telling you to ignore tangential acceleration. The only force on the ball (except for mg) is the static friction. That's what you are asked to compute.

 

[kplooksafterme]

But how can I compute the tangetial static friction force? I can find the normal force and therefore the max static friction, but this isn't necessarily the force that's acutally working on it. I really don't know how to compute this...

 

[Dick]

If the ball maintains a constant rotational velocity, there is NO TANGENTIAL ACCELERATION. You can't compute it. IGNORE IT. Static friction is a multiple of the normal force. Normal force is perpendicular to tangential motion. There isn't any tangential component.

 

[kplooksafterme]

So the only static friction force is the vertical component which is equal in magnitude to the weight?

 

[kplooksafterme]

Ahh, I got the right answer but I'm still a bit confused. I thought that the actual force working on a rolling ball was static friction...

 

[kplooksafterme]

I think I also confused the rotational velocity of the ball with the rotational velocity of the ball moving around the cylinder. So the rotational velocity given in this question refers to the ball rotating about its own center of mass rather than the ball rotating around the center of the cylinder?

 

[kplooksafterme]

Thanks a lot for your help btw...

 

[Dick]

Static friction doesn't do any work on the ball. It just glues it to the wall. But yes, the only relevant frictional force in purely rolling motion is static.

 

[Dick]

I think I also confused the rotational velocity of the ball with the rotational velocity of the ball moving around the cylinder. So the rotational velocity given in this question refers to the ball rotating about its own center of mass rather than the ball rotating around the center of the cylinder?

If you think about it, if the ball is not sliding (that would be kinetic frictional force), both rotational velocities will be the same. You're welcome!