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Easy Java Simulations (2001- ) => Dynamics => Topic started by: Fu-Kwun Hwang on October 10, 2010, 10:06:28 am



Title: Newton's cradle
Post by: Fu-Kwun Hwang on October 10, 2010, 10:06:28 am
The following show animation for Newton's cradle
(http://www.phy.ntnu.edu.tw/ntnujava/index.php?action=dlattach;topic=1976.0;attach=3745;image)
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[ejsapplet]


Title: Re: Newton's cradle
Post by: Fu-Kwun Hwang on October 10, 2010, 10:11:12 am
The following is a real simulation of Newton's cradle (it does collision calculation between balls).

You can select an ID with slider, then change it's mass to check out what will happen when mass are not the same.
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[ejsapplet]
However, the xml did not work properly with latest EJS. If you want to run it offline, please download the attached jar file.

The above two applets were created in 2008. But I only post it at my Chinese web site. 牛頓擺模擬動畫 (http://www.phy.ntnu.edu.tw/demolab/phpBB/viewtopic.php?topic=19870)


Title: Re: Newton's cradle
Post by: Fu-Kwun Hwang on October 10, 2010, 11:38:36 am
There is a better version : Ejs Open source Newton's Cradle java Applet by Paco customized by lookang (http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=824)


Title: Re: Newton's cradle
Post by: ahmedelshfie on October 11, 2010, 11:02:04 pm
Hi prof Hwang
Have a way to organize sound to appear with movement in Newton's cradle java applet customized by lookang,
I would like to translation to portages version for publish.
But first i wish if have a way to organize sounds in applet for no mix students.
thanks prof 
 


Title: Re: Newton's cradle
Post by: mhmdkl on November 26, 2010, 07:12:30 pm
hi
i wonder: how the energy transfers from ball to another?

and do balls vibration after period of time??how?

 if put the newton's cradle in the water, what's happened?? and how it works in water?

and thanks :)


Title: Re: Newton's cradle
Post by: Fu-Kwun Hwang on November 26, 2010, 09:24:30 pm
Newton's  cradle are series of collision between two balls.
If the mass of all the balls are exactly the same, the energy will transfer from one side to another side (from one ball to the next one, ...). If the mass are not exactly the same , it is possible to cause all the ball moving (is this what you called vibration?)

Quote
if put the newton's cradle in the water, what's happened?? and how it works in water?
I would suggest you do the experiment and find out the ANSWER by yourself ;).


Title: Re: Newton's cradle
Post by: mhmdkl on November 26, 2010, 10:42:34 pm
Quote
If the mass of all the balls are exactly the same, the energy will transfer from one side to another side (from one ball to the next one, ...).
yeah i know that ,but Is there a physical equation simulate the transfer of energy?? and how it can be programmed?? :)
Quote
If the mass are not exactly the same , it is possible to cause all the ball moving (is this what you called vibration?)
no, when i saw the lookang's project(newton's cradle) i saw the balls vibration after the period of time?how?

Quote
I would suggest you do the experiment and find out the ANSWER by yourself ;).

ok i'll try ;)


Title: Re: Newton's cradle
Post by: Fu-Kwun Hwang on November 27, 2010, 09:41:37 am
You are welcomed to check out Collision between two pendulums (http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=711.0) or 1D collision : Conservation of Momentum (http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=5.0)

The velocity of two objects after collision ($V'_1,V'_2$)can be calculated from velocity before collisions ($V_1,V_2$) and mass of two objects ($m_1,m_2$).

From conservation of momentum
 $m_1 V_1+m_2 V_2=$ $m_1 V'_1+m_2 V'_2 $,
and conservation of energy $\tfrac{1}{2}m_1V_1^2+\tfrac{1}{2}m_2V_2^2=\tfrac{1}{2}m_1V_1'^2+\tfrac{1}{2}m_2V_2'^2$
So $m_1 (V_1-V_1')=m_2(V_2'-V_2)$
and $\tfrac{1}{2}m_1 (V_1^2-V_1'^2)=\tfrac{1}{2}m_2 (V_2'^2-V_2^2)$, which means $\tfrac{1}{2}m_1 (V_1-V_1')(V_1+V_1')=\tfrac{1}{2}m_2 (V_2'-V_2)(V_2'+V_2)$
So $V_1+V_1'=V_2'+V_2$

i.e. The equation need to be solved are
$m_1 V_1'+m_2 V_2'=$ $m_1 V_1+m_2V_2$ and $V_2'-V_1'=V_2-V_1$

The result is
$V'_1= \frac{m_1-m_2}{m_1+m_2} V_1 +\frac{2m_2}{m_1+m_2}V_2=V_{cm}+\frac{m_2}{m_1+m_2}(V_2-V_1)=2V_{cm}-V_1$
and $V'_2=\frac{2m_1}{m_1+m_2}V_1+\frac{m_2-m_1}{m_2+m_1}V_2=V_{cm}+\frac{m_1}{m_1+m_2}(V_1-V_2)=2V_{cm}-V_2$
where  $V_{cm}=\frac{m_1V_1+m_2V_2}{m_1+m_2}$

It means that $V'_1-V_{cm} = - (V_1-V_{cm})$ and $V'_2-V_{cm}= - (V_2-V_{cm})$
 or $V'_{1cm}= -V_{1cm}$ and $V'_{1cm}= -V_{1cm}$ where $V'_{1cm}=V'_1-V_{cm}$ ...etc.
From the point of center of mass coordinate system: both particles bounce back with the same speed (relative to center of mass).


Title: Re: Newton's cradle
Post by: mhmdkl on November 28, 2010, 04:04:20 pm
Quote
where  $V_{cm}=\frac{m_1V_1+m_2V_2}{m_1+m_2}$

thanks
but what is Vcm? i didn't know it?


THE BALLS IN THE MIDDLE VIBRATE AFTER PERIOD OF TIME ??? WHYY?


Title: Re: Newton's cradle
Post by: Fu-Kwun Hwang on November 28, 2010, 09:58:46 pm
$V_{cm}$ is the velocity for the center of mass. Check out high school textbook or wikipedia.
Quote
THE BALLS IN THE MIDDLE VIBRATE AFTER PERIOD OF TIME
If you referer to the second simulation: It is due to numerical error in the simulation.