__Newton's cradle__by:hwangat 2010/10/10 11:06The following show animation for Newton's cradle

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[ejsapplet]

See 9 replies click__Re: Newton's cradle__by:hwangat 2010/10/10 11:11The 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. [url=http://www.phy.ntnu.edu.tw/demolab/phpBB/viewtopic.php?topic=19870]???????[/url]__Re: Newton's cradle__by:hwangat 2010/10/10 12:38There is a better version : Ejs Open source Newton's Cradle java Applet by Paco customized by lookang__Re: Newton's cradle__by:ahmedelshfieat 2010/10/12 00:02Hi 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

__Re: Newton's cradle__by:mhmdklat 2010/11/26 20:12hi

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 :)__Re: Newton's cradle__by:hwangat 2010/11/26 22:24Newton'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?)

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

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I would suggest you do the experiment and find out the ANSWER by yourself ;).__Re: Newton's cradle__by:mhmdklat 2010/11/26 23:42[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, ...).

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yeah i know that ,but Is there a physical equation simulate the transfer of energy?? and how it can be programmed?? :)

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If the mass are not exactly the same , it is possible to cause all the ball moving (is this what you called vibration?)

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no, when i saw the lookang's project(newton's cradle) i saw the balls vibration after the period of time?how?

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

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ok i'll try ;)__Re: Newton's cradle__by:hwangat 2010/11/27 10:41You are welcomed to check out Collision between two pendulums or 1D collision : Conservation of Momentum

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).__Re: Newton's cradle__by:mhmdklat 2010/11/28 17:04[quote]

where $V_{cm}=\frac{m_1V_1+m_2V_2}{m_1+m_2}$

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thanks

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

THE BALLS IN THE MIDDLE VIBRATE AFTER PERIOD OF TIME ??? WHYY?__Re: Newton's cradle__by:hwangat 2010/11/28 22:58$V_{cm}$ is the velocity for the center of mass. Check out high school textbook or wikipedia.

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THE BALLS IN THE MIDDLE VIBRATE AFTER PERIOD OF TIME

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If you referer to the second simulation: It is due to numerical error in the simulation.