# 01 Super Balls, Double Ball Drop 
    
## Aim   
 Showing that when a superball of small mass resting on top of a superball of large mass is dropped from a low height, the small ball ideally rebounds to nearly nine times its original height.    
  
## Subjects   
* 1E10 (Moving Reference Frames) 
* 1N20 (Conservation of Linear Momentum)   
  
```{iframe} https://www.youtube.com/embed/Oxte-YmnnHI?si=PzP00e48WqzlzpsX
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## Diagram   
   
```{figure} figures/figure_0.png
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:label: 1e1001_figure_0.png  

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```{figure} figures/balls.jpg 

figclass: margin
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:label: 1e1001_figure_X.png

The Astro-superball 
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## Equipment   
 *  1 superball of large mass (basketball). 
 *  1 superball of small mass (table-tennis ball). 
 *  Astro-superball
      
## Presentation   
A superball of small mass is dropped and rebounds almost to its original height. Next, the small superball is held about $10~\mathrm{cm}$ above a larger superball. This combination is dropped simultaneously, and after striking the floor, the small ball launches upward and can reach a height up to nine times the original dropping height. 

```{iframe} https://www.youtube.com/embed/CwEtNIKSpgw?si=kW0gLhwYfTybhISO
```

## Explanation   
Just before striking the floor, both balls have a velocity $v$ downward. Just after the combination hits the floor, the larger ball rebounds upward with a velocity $v$, while the smaller ball is still moving downward with a velocity $v$. This makes their relative speed $2v$ — the small ball is approaching the large ball at $2v$. If the collision between the balls is elastic, the smaller ball will rebound with a velocity of $2v$ relative to the larger ball, but in the opposite direction. Since the larger ball is moving upward at $v$, the small ball’s velocity relative to the floor becomes $v + 2v = 3v$ upward.(See {numref}`Figure {number} <1e1001_figure_1.png>`)

```{figure} figures/figure_1.png
:width: 70%  
:label: 1e1001_figure_1.png

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The small ball would have gone up with a velocity $v$ if it had just hit the floor, but now it takes off with a velocity $3v$. Because $m g h=1 / 2 m v^{2}$, a 3 times higher take-off velocity means that it goes 9 times higher.      


## Remarks
*   Do not rest the table-tennis ball on the basketball and drop it in such a combination. When this is done, the table-tennis ball stays fixed to the basketball (aerodynamic reason), and for this demonstration, it is required that on hitting the ground, there is some distance between the two balls. 
*   It is recommended to practise the drop beforehand, especially to ensure that the small and large balls are released simultaneously.
*   An extension of the demonstration is to drop a stack of three or even more balls (See {numref}`Figure {number} <1e1001_figure_X.png>`). When a three-ball combination is dropped, the top ball approaches a maximum of 49 times the initial release height. In order to drop the Astroball-stack perfectly vertical, wet your fingers holding the stack and slowly let it slip away. 
*   The experiment does not perform very well on a wooden floor.
   
  
## Sources   
 
*  The Physics Teacher, vol. 21, no. 7, pag. 466, Superball problem, G. Stroink 
*  Ehrlich, Robert, Turning the World Inside Out and 174 Other Simple Physics Demonstrations, pag. 60 
*  Stark Verlag, Astro-Blaster 11938