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Why friction plays no role in this non-slipping billiard ball problem?

  • Thread starter andresB
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Homework Statement:

Consider the following exercise

Relevant Equations:

.
245504


===================

Now, I can get the solution in the book by writing and solving the force and the torque equations together with the non-slipping relation between the angular acceleration and the center of mass acceleration. However, the book solution only arises if there no friction between the ball and the table.

I don't get why friction is not taken into account.
 

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  • #2
haruspex
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Problem Statement: Consider the following exercise
Relevant Equations: .

View attachment 245504

===================

Now, I can get the solution in the book by writing and solving the force and the torque equations together with the non-slipping relation between the angular acceleration and the center of mass acceleration. However, the book solution only arises if there no friction between the ball and the table.

I don't get why friction is not taken into account.
It's to do with (the theoretical treatment of) sudden impulses.
The impact is taken as consisting of an arbitrarily large force acting for an arbitrarily brief time. Only the product of these, the momentum, is knowable.
The friction between the ball and the table is limited by ##\mu_smg##. Over the arbitrarily short period of the impact, that can only exert an arbitrarily small impulse, so can be ignored.
The situation is different if there is a vertically downward component to the delivered impulse, since there will be a corresponding component to the normal force, and hence to the frictional force.
 
  • #3
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So, the idea is that in the short duration of the hit, the force (horizontally) hitting the ball is just much bigger than the static friction. Is that an accurate assumption in the case of actual billiard balls and tables?
 
  • #4
haruspex
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So, the idea is that in the short duration of the hit, the force (horizontally) hitting the ball is just much bigger than the static friction. Is that an accurate assumption in the case of actual billiard balls and tables?
Yes, and yes.
According to http://dbkcues.ru/articles-2/collision-of-billiard-balls/?lang=en, the collision time is around 250-300μs. Plug in numbers for the speed and mass and see what the forces must reach.
 
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