- #1
- 68
- 0
If we set a ball rolling on a loop-the-loop track,why do we say that we need infinite friction coefficient for the ball to complete the loop. This seems illogical because f=kN. Since f and N are finite how can k be infinite ?
Where did you see this statement?If we set a ball rolling on a loop-the-loop track,why do we say that we need infinite friction coefficient for the ball to complete the loop.
If we set a ball rolling on a loop-the-loop track,why do we say that we need infinite friction coefficient for the ball to complete the loop. This seems illogical because f=kN. Since f and N are finite how can k be infinite ?
It just would mean there's no slippage while the ball is rolling. Infinite friction isn't required. You just need enough friction combined with enough speed and the related centripetal force to keep the ball rolling and not sliding, even when at the top of the loop.Wouldn't an infinite coefficient of friction say that you can't move an object at all?
Why do you think this?But if we look at the friction required on inclined plane for rolling it is some function of tan x .
Please show us!Physics says this and it can be proved easily using concept of pure rolling and solving some eqns
Nonsense. If it's so simple, just show us. (I suspect you are mixing up a few concepts or situations.)Just try it once yourself and btw you can find it in any good standard physics book.
OK, I see what you're saying now. That's for rolling down an incline. Note that there is no acceleration normal to the surface, so only the normal component of gravity is available to provide the normal force. So if you have too steep an incline there will not be enough friction to produce rolling without slipping. (Another way of saying that is to claim an 'infinite' coefficient is required, which is clearly unphysical.)Let f be friction.
Then mgsinx-f=ma(linear)
Also equating torque we get
fR=I@(angular acceleration)
and a=R@ for pure rolling
Solving this v get
f=Ia/R^2
And a = gsinx/1 + I/MR^2
So finally we have minimum friction coefficient for pure rolling is tanx/1 + MR^2/I
Your statement about needing an infinite coefficient of friction was based on rolling without slipping down an incline (with infinite slope). The loop situation is different as there is acceleration normal to the surface.Still my query is not solved
Let f be friction.
Then mgsinx-f=ma(linear)
Also equating torque we get
fR=I@(angular acceleration)
and a=R@ for pure rolling
Solving this v get
f=Ia/R^2
And a = gsinx/1 + I/MR^2
So finally we have minimum friction coefficient for pure rolling is tanx/1 + MR^2/I