astroblaster is a set of four ball, aligned vertically. if the balls touch the ground after the multicollisions between the balls, tha higher one is ejected to the height 10 x greater the initial heights was.... Is similar applet somewhere created?

Yes. There is a simulation distributed with EJS which can be adjusted to exactly what you want. So I modified the example and change the parameter to fit with your request. The ratio for the highest height to the initial height will depend on the ratio of the mas. Initially, the mass ratio is 2.0 and the ratio is close to what you have expect (but not quite the same). You can adjust the mass ratio and see what will happen! You can also change the number of particles. And what if the mass ratio is less than 1.0? Ask yourself before you hit play! Have fun!

Dear Fu-Kwun, thank you for info and applet. I try to look on it. Now I am in review of my article to Physics Education about the astroblaster, where I try to explain collisions for rather coefficient of restitutions between the balls, it can be an idea for improvment of the applet....tha mass ratio it can be calculated for specific coefficient of restitution, (ideal case e=1) but in real conditions, if somebody would like to create own one and has the real balls, the exact mass for maximum height can be calculated.... I can show you...if you wish...we can implemented it into the applet... Marián

In the above simulation, k is the coefficient of restitutions between the ball and the wall/ground. I am not sure is it a good ideas to add coefficient of restitutions between the balls.

It will make the simulation more like real case, but it will make it more complicated. Now, students can check that energy is conserved.

For elastic collision: The velocity after collision could be calculated as V1'=(2*m2*V2)/(m1+m2)+(m1-m2)*V1/(m1+m2); V2'=(2*m1*V1)/(m1+m2)+(m2-m1)*V2/(m1+m2);

Actually, for educational purpose, it will be better to ask: how to modify the above equations if we want to add coefficient of restitutions between the balls.

I can add coefficient of restitutions between the balls easily, and if you give me information about the mass/size/... and the experiment data for the real case, may be we can try to find good parameter sets to fit with your data. I would suggest you make a video of the experiment and convert the movie file to quicktime format, then, those data can be analyzed with tracker and compared with ejs simulation.

Dear Fu-Kwun, thanks for your comments about the astroblaster. I look at your applet, it is fine, but your consideration is about the collisions, where the speed of the second ball after the collision is not zero. If we would like to arrange the conditions for the highest throw (what is as much as possible done in case of astroblaster), the balls masses must be specific....Based on it would be suitable to create the applet, where coefficient of restitution between the balls are the same, but it can be see, how it works....the key role is the specific mass for the ball, which depends on coefficient of restitution between the balls. I have some videos, it is not problem to create mov files, and by using the videotracker, compare the real astroblaster with model one. Now we are working on creation of the astroblaster from set of four different balls (football, voleyball, ..) and I like to make the videos, measure the real data....

Dear Fu-Kwun, The mass ratio is the same for all the balls, in the astroblaster simulation. For the maximum height of the astroblaster throw is necessary to apply the different mass ratios between the balls (after the collision it can be possible that lower ball has zero velocity)

I try to add different mass ratio in your astroblaster applet, but some error messages occurs. Could you help me with it?

What I would like to do: - for maximum four balls, to simulate the throw in case of different mass ratios of the astroblaster ball, - we need add mass ratio mr12, mr23, mr34 that: (m2=mr12.m1), (m3=mr23.m2), (m4=mr34.m3), - in applet we need to modify by slider not only mr but : mr12, mr23 and mr34 .

If you will have the time, please help me with it.

I have modified the code according to what you would like to do: You can change the slider to modify mass ratio between different balls. The initial mass ratio are: m2:m1=5./3.; m3:m2=2:1, m4:m3=3:1 Just hit play and you will find out. You can change it to other ratios. -*- If initial mass ratio are 1:2:10:30 (m21=2, m32=5, m43=3) :only the last one will be stopped.

Dear Fu-Kwun, thank you for your help with astroblaster applet. I try to learn from the code, how you create rather mass ratios...I would like to show advantage of this idea. If we set m2:m1=1,66, m3:m2=2, m4:m3=3, (for k=1) lowest three balls are in the rest after the collisions (see dialog window, or switch off auto scale) and height of the throw is greater than in case of constant mass ratio = 2.

Dear Fu-Kwun, I try offline version, all is OK. But the downloaded .xml file produce another version of the astroblaster applet (without slider for mass ratios). Please look on it and change it or explain me, where I`m wrong. Thank you, Marian

Amazing. The last three balls are all stopped, and only the top one move up when I tried with parameters from previous message. Sorry. May be I did not update the latest xml file to the server. However, the source is at home. I will update to the server tonight.

It is the idea of my approach in this applet. In case when three balls are in the rest after the collision, their initial energy is transfer to the top one. The height of the throw must be (is) greater then before - (when we have constant mass ratio=2 and balls are in multicollisions). It can be shown by the applet. Now, I would like to see if my calculation gives the same height as applet.

This state is for k=1. But which mass ratio is necessary for the same state in case of k<1. I prepare mathematical solution for mass ratio dependence on coefficient of restitution. It can be next step in this applet.

I forgot to save the ejs source after I modified the code. That is the reason why the previous downloaded source did not work. So I have to modify the code again, and it should works fine now. The initial values for mass ratios are modified as (5/3. , 2.,3. -- according to your result.)

The applet also shown the total energy (kinetic energy+potential energy) for all the balls, you will find out that there is only a very small change during the simulation(numerical error range).