Re: what would happen to a soccer ball if you put helium into it

The short answer is nothing much.  

This was actually studied in footballs, not soccer balls :0
There were theories based on suspected use of helium and the inflation gas 
instead normal air.  So a group of engineers and scientists found a 
college kicker who was willing to participate.  The difference in weight 
of the inflating gas is insignificant when compared to the mass (weight) 
of the ball bladder and skin.  


Let's consider kicking a ball as kinematic collision. I will assume that 
the ball's "bounciness" will be the same no matter which gas has been used 
to fill it.  Let's also consider a ball that is stationary before being 
kicked.

The speed of the ball after the collision with the player's foot depends 
on the momentum generated by the player's foot that is transferred to the 
ball.  We can also look at this collision in terms of impulse force 
imparted on the ball over the very short time of the collision (kick).  If 
the everything is the constant with the kicker's impulse imparted to the 
ball then a lighter ball will start out with a greater initial speed.  For 
a given angle of launch, a projectile will travel farther as the initial 
speed increases.


The other important forces at work are lift and drag.  
The drag force for the ball travelling through the air is independent of 
the mass of the ball and dependent on properties of the air, geometry of 
the ball, and speed of the ball relative to the air.  Lift is similar but 
also has effects from spin that causes differences in air flow around the 
ball.


What we need to consider is the ratio of the terms based on mass (gravity 
and initial speed) versus terms that depend on interaction with moving 
through the air (fluid mechanics) that are dependent on relative speed, 
air density, and geometry of the ball.

We know that a lighter ball will have greater speed than a heavier ball 
after a kick if everything else is kept constant. Consider an extreme 
example, a person can probably kick a small soccer ball much faster than a 
heavy basketball or playground ball.

In general, I suspect that lift is not a huge term for a soccer because 
the rotation of a soccer ball is pretty slow for most kicks. (The ball can 
have significant spin for slicing or hooking kicks.)  So let's ignore 
lift. 

Because drag does not depend on mass of the ball it should be the same no 
matter what is filling the ball. 


So what happens?  
Consider an extreme example again.  Suppose we apply the same sort of 
logic to the difference between a baseball and a wiffle ball that are 
struck the same way by a baseball bat.  The wiffle ball will probably have 
a higher speed off the bat compared to the baseball because it is much 
lighter than the baseball.  However, the drag and lift will much for 
significant for the wiffle ball than the baseball once it is in flight. 
Therefore, the wiffle ball loses its momentum faster to the drag force of 
the air and is more subject to lift or wind gusts. 

How much lighter is a soccer ball filled with helium versus one filled 
with air as a percentage of the overall weight?  I am guess much less than 
5%.  So the differences in flight of the ball are going to be small.  
Small enough that they are likely to go unnoticed. 


For more details, see The Physics of Football by Timothy Gay or search the 
Mad Scientist database for previous answers on the interaction of air on 
balls or other objects moving through the air or water (keywords: drag, 
speed).

Sincerely,

Tom "Wiffle King" Cull

P.S. Both whiffle and wiffle are considered correct spellings. I don't 
know if one is trademarked.