- #1
JuanC97
- 48
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A. The problem: (If you want the short version just read the underlined statements)
I need to describe the motion of a cue ball over the cloth of a billiard table.
For rule, I can't use equations for rotational motion or 'Work and Energy theorems'. I have some ideas but I'm not sure about the concepts and procedures. I'd appreciate it if you take a look to my reasoning and give me some pieces of advices (I'm just trying to describe traslation)
B. Relevant equations:
Friction force due to bearing (Rolling resistance): Frr = Crr* N
Crr is the Rotational resistance coefficient ; N is the Normal force.
Dynamic (Kinetic / Sliding) friction: Frd = μd * N
C. The attempt at a solution: (Reasoning)
See the first Image: The white ball is at rest. There are frictional forces.
The cue hits the ball in its center of mass and the force it's aplied parallel to the plane.
Because of the motion it will be a frictional force acting opposite the movement but...
Here's the problem: the ball will roll or it will slide ? (What kind of friction goes into the equations?)
I think these are the most probable situations:
1. The cue hits the ball and its motion is Pure sliding. A few meters later, the motion is pure rolling.
2. The cue hits the ball and its motion combines Sliding and rolling. Then, is just pure rolling.
D. The questions:
* In both cases I have to calculate the distance traveled before starting to roll purely. How?
* How can I find an expression of the minimum force needed to make each of those possiblities real?
It's my first question in PF.
I will appreciate every hint and piece of advice that you could give me. :)
I need to describe the motion of a cue ball over the cloth of a billiard table.
For rule, I can't use equations for rotational motion or 'Work and Energy theorems'. I have some ideas but I'm not sure about the concepts and procedures. I'd appreciate it if you take a look to my reasoning and give me some pieces of advices (I'm just trying to describe traslation)
B. Relevant equations:
Friction force due to bearing (Rolling resistance): Frr = Crr* N
Crr is the Rotational resistance coefficient ; N is the Normal force.
Dynamic (Kinetic / Sliding) friction: Frd = μd * N
C. The attempt at a solution: (Reasoning)
See the first Image: The white ball is at rest. There are frictional forces.
The cue hits the ball in its center of mass and the force it's aplied parallel to the plane.
Because of the motion it will be a frictional force acting opposite the movement but...
Here's the problem: the ball will roll or it will slide ? (What kind of friction goes into the equations?)
I think these are the most probable situations:
1. The cue hits the ball and its motion is Pure sliding. A few meters later, the motion is pure rolling.
2. The cue hits the ball and its motion combines Sliding and rolling. Then, is just pure rolling.
D. The questions:
* In both cases I have to calculate the distance traveled before starting to roll purely. How?
* How can I find an expression of the minimum force needed to make each of those possiblities real?
It's my first question in PF.
I will appreciate every hint and piece of advice that you could give me. :)