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Toppling problem

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tiny-tim

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I honestly don't get this, why the force is minimum when you use the rolling constraint? :confused:
rolling is defined as a = rα

anything else isn't rolling

if you gradually decrease F (for a particular µk) until you get rolling, the minimum F will be when rolling occurs, ie a = rα :smile:

(hmm … or maybe we should increase F, and use the rolling equations, and find the value of F for which the friction equals µsmg ? :confused:)
 
3,810
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rolling is defined as a = rα

anything else isn't rolling

if you gradually decrease F (for a particular µk) until you get rolling, the minimum F will be when rolling occurs, ie a = rα :smile:

(hmm … or maybe we should increase F, and use the rolling equations, and find the value of F for which the friction equals µsmg ? :confused:)
Let me state the problem once again.

A solid sphere (or a billiard ball) is at rest on a rough horizontal surface with coefficient of friction ##\mu_k##. A force acts below the CM at a distance R/4. Find the minimum force required so that the sphere backspins. (I hope I wrote the problem correctly.)

In case of backspin, the friction acts backward. The equations I have posted before are still valid.

I was thinking that I will have to deal with impulse. I guess the problem is poorly worded.

Please modify the problem statement as you wish. :)
 

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tiny-tim

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if you start with small F, the ball will roll

if you gradually increase F (until rolling stops), you will get the equations i mentioned, with the condition involving µs

however, if you start with large F, the ball will slide

if you gradually decrease F (until rolling starts), you will get the equations i mentioned, with the condition involving µk
I was thinking that I will have to deal with impulse.
i think what really matters is the force

if during the impulse the maximum force is enough to produce sliding, then the ball will slide
 
3,810
92
if you start with small F, the ball will roll

if you gradually increase F (until rolling stops), you will get the equations i mentioned, with the condition involving µs

however, if you start with large F, the ball will slide

if you gradually decrease F (until rolling starts), you will get the equations i mentioned, with the condition involving µk


i think what really matters is the force

if during the impulse the maximum force is enough to produce sliding, then the ball will slide
Thank you very much for the help tiny-tim! :smile:
 

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