Bowling Ball Problem: Is Friction Force All Absorbed in Rotation?

[dean barry]

Im trying to build a behaviour model for the process.
The 5/7 was a stab in the dark, i had attributed 50:50 friction force distribution but it didnt work, but the 2/7 losses thing fell into place when i did.
I had assumed full friction force throughout.
But if at the outset full friction force applies and then diminishes to zero at synchronous speed:
The work done by friction in this distance is ( friction force / 2 ) * distance.
The remaining KE (at synchronous speed) = 5/7 of the original
Ill build the model using these parameters and see how it looks.
Thanks for your patience.

 

[dean barry]

According to my model, modified as described:
(m = 10 kg, g = 9.81 m/s/s, k = 0.1, r = 0.1, initial v = 10 m/s)
distance to synchronous speed = 28.57 m

 

[sophiecentaur]

Im trying to build a behaviour model for the process.
The 5/7 was a stab in the dark, i had attributed 50:50 friction force distribution but it didnt work, but the 2/7 losses thing fell into place when i did.
I had assumed full friction force throughout.
But if at the outset full friction force applies and then diminishes to zero at synchronous speed:
The work done by friction in this distance is ( friction force / 2 ) * distance.
The remaining KE (at synchronous speed) = 5/7 of the original
Ill build the model using these parameters and see how it looks.
Thanks for your patience.

This is the wrong way round. The friction force will be highest (static friction) when the relative speeds between periphery and ground is zero. Whilst there is slippage, the friction force could well be less (sliding friction) but it's easier to assume there's no change. The fact that the force is constant allows you to assume that the angular acceleration is constant in the calculations. If the force diminished to zero, the ball would never stop slipping - just getting slower and slower at an ever slower rate.

 

[dean barry]

Thanks sophie, I've a better understanding of this problem, though a movie would be a great help.
Appreciate all the assistance.

 

[sophiecentaur]

Thanks sophie, I've a better understanding of this problem, though a movie would be a great help.
Appreciate all the assistance.

The idea is to try to run the movie in your head! So many simulations are so slick that it's easy to miss the key issues in the sensory overload. The secret is always to apply the 'rules', like Momentum Conservation. Some personal solutions can ignore those rules and lead you up 'that' creek with no paddle. I'm glad that you're sticking with it! nYou will get all the way, eventually.

 

[dean barry]

OK sophie, thanks for your help.
I confess to being somewhat overwhelmed by the response.
Im baffled by your previous post : Friction force is highest when the relative speed is zero (ie synchronous speed)
I assumed that at that point only rolling resistance was present.
Anyhow, ball enters stage left at given constant velocity (ill use 10 m/s) with rotation zero.

Its sliding so linear retardation takes place (not through translation), as it would do in the case of a block sliding.
A torque is applied also so rotational acceleration takes place.

My model assumes that the ball actually acts like part block and part ball, are you with me ?

 

[sophiecentaur]

OK sophie, thanks for your help.
I confess to being somewhat overwhelmed by the response.
Im baffled by your previous post : Friction force is highest when the relative speed is zero (ie synchronous speed)
I assumed that at that point only rolling resistance was present.
Anyhow, ball enters stage left at given constant velocity (ill use 10 m/s) with rotation zero.

Its sliding so linear retardation takes place (not through translation), as it would do in the case of a block sliding.
A torque is applied also so rotational acceleration takes place.

My model assumes that the ball actually acts like part block and part ball, are you with me ?

Yes, of course you are right that the force is zero when there's no relative movement (I guess that would be an instantaneous value) but, when there is movement, I can't see how the force can be any less than the limiting friction as the relative speed is non zero. This assumes that sliding friction is no different from static friction, of course. My reason for saying this is that I can't think what other value it could take than μmg. When a block slides along a surface, this force acts all the time. If μ is high then the acceleration is high (negative). If, as you suggest, the force gets less and less, then you could have the situation where the ball never stops slipping. Is that possible / likely/ according to experience? I am considering the most ideal case here.

 

[dean barry]

Have you any comments on the friction loss = 2/7 of the original KE ?

 

[sophiecentaur]

Actually, using conservation of angular momentum, I find that the velocity will drop to 5/7 of original.
Initial L = mrv
Final L = mrv' + 2mv'/5
etc. to give v' = 5mv/7
Which means a loss of 2/7 of velocity. That much has to be right, I think, as it's so straightforward (?).
To find loss of KE:
Original KE = mv²/2
Final KE = Linear KE + angular KE
= m( (5v/7)² + ((2X5)v/(5X7))²)/2
and I can't find anything wrong with that either.
And that suggests that the final KE is 29/49 of original
So the 2/7 loss answer really doesn't seem to fit.

 

[dean barry]

Thanks sophie, ill be back 12 noon GMT tommorow.