Effects of Friction on Deceleration.

[Heffe6]

I've nothing more than one high school class and a curiosity in physics, and I'm sure this is a simple, albient random question. Its something I was discussing with some friends the other day, and I'd like some legitimate input, instead of our uninformed guessing.

Thanks to all who read and post. I'll just kinda of talk though it and maybe someone can let me know if I am correct.

In the case of a ball rolling along the ground, friction causes the ball to slow down and eventually come to a stop. My question is, Does the ball decelerate at a constant speed, or does the ball decelerate at the beggining more quickly than at the end. Seems to me that the deceleration would be uniform since the friction comes from the force of gravity acting on the ball, and that remains constant.

Next take the example of a ball rolling horizontally along the inside of a tube perpedicular with the ground. There is a force of gravity here as well, but I wouldn't think it is contributing to the deceration of the ball. The friction and deceleration is caused by the centriugal force of the ball against the inside of the tube. So it seems that the force is not constant, as it depends on the mass of the ball as well as the speed that it is travelling. So, in this case, the ball would decelerate more quickly at the beggining when it is traveling faster, and more slowly towards the end.

I guess the main question is, is my assement correct? Also, if it is correct, is there an equation that could be used to find at what point the ball rolling along the inside of the tube would come to a stop (horzontally) taking into account the varying force of friction?

Thanks to all who read and answer this question, I've just recently found this site, but it seems there's such a weath of information! Oh and sorry for any spelling errors, I'm in a foreign country right now, and the spell checker says every word is mispelled.

 

[rjbeery]

Heffe: I don't understand your second example, but I believe that in your first example the deceleration will be uniform until the ball is close to its stopping point. When you apply your car's brakes with constant pressure, notice that there is an additional forward thrust to the passengers just as the vehicle comes to a stop. This is because static friction requires more force to overcome, so it absorbs more forward momentum. However, dynamic friction is unaffected by speed (according to Coulomb's Law of Friction), so if we ignore static friction the deceleration of the ball should be uniform.

I am certainly not an expert on this though, and I may be wrong. You should research "Tribology".

 

[Dr.D]

In your first case, you said, "Seems to me that the deceleration would be uniform since the friction comes from the force of gravity acting on the ball..." This is not really true. The ball is rolling on the ground, and the force of gravity acts perpendicular to the surface of the ground (toward the center of the earth). This does not act to slow the ball. The friction forces that eventually cause the ball to stop arise from deformation of the surface due to the weight of the ball (something that is constant) which may be slightly affected by the velocity (which is not constant), and from the air friction which is not constant. Also, tiny irregularities in the surface will tend to slow the ball down because each encounter with an irregularity will result in a plastic impact, resulting in a loss of energy.

Your second case I cannot follow when you talk about "ball rolling horizontally along the inside of a tube perpedicular with the ground." I don't understand how we can have a ball rolling horizontally in a tube perpendicular to the ground.