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 Author Topic: Motion of a Ping-Pong  (Read 112788 times) 0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).
Fu-Kwun Hwang
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 « Embed this message on: January 29, 2004, 03:25:19 pm » posted from:,,Satellite Provider

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Have you ever use your finger to press down one side of the ping-pong ball?
If you press hard enough, you will find ping-pong ball running away from you.
However, a few seconds later, the ping-pong starts to rolling back toward you. Why?

The ball starts with an initial velocity Vo, and an initial angular velocity wo.
Due to the friction force between ping-pong ball and the table
Fu=u mg. (Blue arrow)
The center of mass of the ping-pong ball will slow down.
V= Vo - a t

The friction force will produce a torque ( r u mg, where r is the radius of the ball ) to change its rotating speed w = wo-t * (r u mg)/I.
where I is the moment of inertia of the ball.
When the velocity of the contact point related to the table V - r w becomes zero, the friction force vanishes.

The motion become a free rolling (rolling without slipping). V = r w
if V< 0. then ping-pong ball rolling backward (toward you).
Is it passible to let the ball stop? (velocity V=0.) or moving forward(V>0.)?
Under what kinds of conditions? This java applet let you play with it. Enjoy!

The initial velocity of the ball is fixed. Vo= 200. cm/s.
You can change different initial angular velocity wo ( r*wo was shown).
r*wo<0 : counterclockwise, r*wo>0 : clockwise

Press start button to starts the java animation.

RightClick the mouse button to toggle the animation. The white arrow below the ball represent the friction force.
Press Clear to clear the curves (Velocity V verses time t).

 red velovity at the center of mass green angular velocity * radius ( w* r) yellow free rolling V = r * w

You can also change the friction coefficient u.

How to calculate?
1. What is the friction force between the ball and the table?
2. What is the acceleration of the ball¡H How the speed changed?
3. What is the torque to the ball? ¡HHow the angular velocity changed?
4. What is the velocity of the contact point relative to table?

Can you write down the equations of motion ?
¡]The momentum of initial for the hard sphere ball is I= (2/5) m r2, I= (2/3)mr2 for thin spherical shell )

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There are 3 translations,
Higher number at the end means more translation been done.
or
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Andre Michelle
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 « Embed this message Reply #1 on: January 17, 2006, 04:32:43 pm »

hi hwang,

i'm currently developing a pinball engine where the ball should move with respect to its rotation. I'm not that familar with mathematical notation, so I hope that you can explain some of the letters, you are using here. I'm trying to explain it for myself, so you may just correct me, if I'm wrong. These are beginner questions, but your execution fits perfectly to my current problem. Don't bother

Fu=u mg:

m,g is mass, gravity.
Fu is the force, that acts to the ball, while he is rotating in a different speed than his linear velocity (friction). Is 'u' the velocity at the contact point (ball, table) ? Is 'u' a vector ?

V= Vo - a*t:

a is not more than just subtracting Fu with respect to time ?

w = wo-t * (r u mg)/I:

w is the angularVelocity, w0 is the old angularVelocity minus ( radius * u * mg ) / inertia with respect to time 't'.

I wonder, if there are any if-conditions in your source or are the forces clearing for theirself ?
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Fu-Kwun Hwang
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 « Embed this message Reply #2 on: June 10, 2010, 03:37:57 pm » posted from:Taipei,T'ai-pei,Taiwan

Here is the EJS version of the same applet.
The blue arrow represents the friction force, while red arrow is the velocity vector.
The red trace represents Vx as a function of time Vx(t), while green trace represents $R*\omega$ of the ping-pong ball.
When $R*\omega$ equal to Vx, the ping-pong ball become rolling without slipping (And the slide friction disappear).

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• Please feel free to post your ideas about how to use the simulation for better teaching and learning.
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Let's work together. We can help more users understand physics conceptually and enjoy the fun of learning physics!

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hemmrao
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 « Embed this message Reply #3 on: July 11, 2010, 11:36:45 am » posted from:Dharwad,Karnataka,India

I can't see the image to simulation, please correct it, thanks and great -*- physics game . .
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ahmedelshfie
Ahmed
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 « Embed this message Reply #4 on: July 11, 2010, 11:24:54 pm » posted from:Uberaba,Minas Gerais,Brazil

You need to click by mouse on eye image (left click) and applet,
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lookang
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http://weelookang.blogspot.com

 « Embed this message Reply #5 on: September 22, 2010, 11:20:51 am » posted from:SINGAPORE,SINGAPORE,SINGAPORE

Here is the EJS version of the same applet.
The blue arrow represents the friction force, while red arrow is the velocity vector.
The red trace represents Vx as a function of time Vx(t), while green trace represents $R*\omega$ of the ping-pong ball.
When $R*\omega$ equal to Vx, the ping-pong ball become rolling without slipping (And the slide friction disappear).

Click the following image to view the simulation.

[ejsapplet]

the omega_i = 60 is always stuck.
need to edit the codes to enable the ability to vary the initial angular velocity for a more power simulation!
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Fu-Kwun Hwang
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 « Embed this message Reply #6 on: September 22, 2010, 02:43:56 pm » posted from:,,Taiwan

Thank you for the bug report!
The bug is fixed and the applet is updated!
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lookang
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 « Embed this message Reply #7 on: September 22, 2010, 08:08:14 pm »

hi prof
i found some bugs
5 fix bug in equation d(omega)/dt = kv*kw*mu*g/R, kw missing
11 fix bug the trace is position correctly now at the fixed point on the rim of the object

i also improved it here http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1953.0
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1953.0
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Fu-Kwun Hwang
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 « Embed this message Reply #8 on: September 23, 2010, 04:59:39 pm » posted from:Taipei,T'ai-pei,Taiwan

Thank you for the bug fixed and improving of the applet!
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Wisdom is to form a good attitude and a healthy lifestyle. ...Wisdom