Does the average density of a ball affect its bounce height? I'm in the IB program in my high school, and we are doing an internal assessment in physics. It must be about some physical property of a bouncy ball. I decided to determine how the average density of a ball affects its bounce height. Does density actually affect bounce height, or am I starting a lab that is pointless?
 A: I think this is a pointless lab activity because density is not something which can be varied easily without affecting other properties such as elasticity and diameter - eg by choosing a different type of ball. 
Although it is gratifying to come up with an original line of research, an easier and more reliable strategy is to build on the work of others at your school - which is what usually happens in academic/industrial research. Find out what projects have been done before, and look for ways of improving on them. Most projects contain evaluations which point out shortcomings in the method and include suggestions for future research.
If you are still stuck for ideas, "The Physics of Basketball" cited by akhmeteli contains quite a few suggestions. After a little digging on the internet I found :


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*confirming the law of reflection for a ball bouncing off a surface, and investigating the effect which spin has on reflection angle (http://www.sciencebuddies.org/science-fair-projects/project_ideas/Phys_p039.shtml)  

*measuring coefficient of restitution as a function of diameter of balls made of the same material ( http://aapt.scitation.org/doi/abs/10.1119/1.4902196?journalCode=pte)
Other ideas :


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*modelling drag on a ball to confirm it is proportional to area and speed or speed-squared;

*measuring the deformation of a ball as a static load is placed on it, to verify that Hooke's Law is obeyed.
Pick a couple of options and discuss them with your teacher.
A: Density does affect the bounce height (to some extent), in particular, due to air drag: the higher the density, the less significant is the effect of air drag.
A: The bounce height tells you about the fraction of energy lost from the moment the ball was dropped, until it has rebounded.
This can include air drag (especially important for very light objects like beach balls), the surface you bounce on (sandy beach or marble floor?) , the degree of deformation of the ball during the bounce (more deformation, like a poorly inflated ball, will lead to greater loss) the actual material of the ball (some materials are more lossy than others) and the nature of the interface between ball and surface (friction can play a part - lower friction can lead to higher bounce).
It may be difficult to use just "density" without the other factors confounding the result (for example, a lower density material might deform more - is it the deformation or the density that caused the difference?). I think inflation pressure of the same ball would be an easier experiment to do successfully. Combine it with an investigation of friction (use sandpaper face-up or face-down, or spray the floor with teflon spray) and you would have an interesting project. You can use a water manometer to determine pressure in the ball with good accuracy.
Have fun.
