I have planned the experiment as so that we can get a whole range of results, and therefore we would need a high height to drop the ball from. Now the problem lies within that the roof height (with a part of the ceiling tile removed is ≈ 3 metres) is quite high and it would be impossible for me to drop the ball at that height, and measure how far it would bounce. Even if I could, there would be the parallax error (even though it may be just a few centimetres each way, that would give an inaccurate result see fig 1.) to contend with. So, I have teamed up with a partner and, while he drops the ball, I will take the reading. We will do the roles exclusively, which means that I will take all the readings, so that there would be no differential operator errors.
[Fig. 1-PARALLAX ERROR]
We will also have to take account the air pressure/materials inside the ball, e.g. the more pressure a tennis ball has inside it, the less surface dents during a bounce and the more of its original energy it stores in the compressed air. But an unpressurised tennis ball-or an old one (as the air inside would have time to diffuse out of it) will bounce less high, as the ball will dent deeply and its skin flexes inefficiently. Much of the ball’s original energy is lost through thermal energy in heating the bending skin and it does not bounce very high. Another reason I have chosen a tennis ball is the fact that in a golf ball, they have layers of different materials and sometimes a liquid core, which are designed to bounce higher. And it is difficult to know whether it is the skin/height that makes it bounce higher or its substance inside the ball.
The ball’s temperature will have to be kept constant, although it will not affect the results very much, however an exaggerated effect of this is seen in squash balls where, the ball has to be warmed to a sufficient degree before playing. This is so that its bounce and hit will be better, and also the fact that squash balls can give a large range of results in different temperatures (another reason to drop squash balls as a test ball).
Any other conditions such as air temperature, air pressure, gravitational conditions, moisture, wind conditions etc will be kept constant so that there would be no discrepancies in the results. Although these factors may seem small, the average experimental error with these minor factors in is ≈ 5%.
Scientific reasoning+prediction: Effect of changing the height of a ball dropped
When you lift a ball off the floor, you transfer energy to it. This energy is stored in the gravitational force between the ball and the earth (gravitational potential energy-GPE) when you release the ball, its weight makes it accelerate downwards at 9.8 m/s (gravity) and its GPE gradually becomes kinetic energy. When the ball hits the floor, both the ball’s surface and the floor’s surface begin to distort, and the ball’s kinetic energy becomes elastic potential energy in these two distorted surfaces. (the fractions of the collision energy stored in the tennis ball and the floor depend on how far each of them dents, the more one dents, the larger the fraction of the collision energy it receives. Also, the ball stores this energy as a compression of the air inside the ball.)
However, some of the original energy (GPE and kinetic) has been converted into thermal energy by internal frictional forces in the ball and the floor. The distorted ball for a moment remains motionless but then it begins to “undent”. Then pushes it and the bent floor apart (ratio of surface push/ball push depends on type of surface and ball-however the floor will never push up on the ball harder than the ball pushes on the floor as that would violate Newton’s third law.) and the ball bounces into the air. Some or most of the elastic potential energy becomes kinetic energy in the ball, and the rising ball then converts this kinetic energy into gravitational potential energy. But the ball does not reach its original height because some of its original gravitational energy has been converted into thermal energy during the bounce.
I predict that a new tennis ball just taken from a pressurised can, will bounce up to 55%-60% of its original height dropped. This is because the tennis ball will behave like a spherical spring, when the ball hits the floor it exerts a force on the floor and the floor exerts a force on the ball. This force compresses the tennis ball-as long as the compression is small then Hooke’s Law will be satisfied. However, because the material the ball is made from is not perfectly elastic then the molecules will reorganize-sliding over one another/bonds broken, and then some of the energy will be lost due to internal like frictions. A perfect elastic material ball will only experience elastic deformation-the molecules in the material do not reorganize, but only changes their relative spacing during the dent. And so will not bounce back to its original height.
However my own tennis ball has been left in a warm cupboard for about a year, this would mean that the air pressure is reduced because the ball loses air by diffusion through the rubber lining. Diffusion is a thermally activated process in which the individual air molecules move between the rubber molecules and migrate through the material and the higher the temperature the diffusion process is speeded up. And so I predict it will bounce to around 40%-45% of its original height, this is because a ball’s bounciness depends on its retaining air inside its rubber shell and mine has been deflated a little also the rubber has decayed a little. This would mean that the rubber is softer, and will not bounce high, as the harder the rubber the molecules are more constrained and will not be able to slide about much.
And so I conclude this section by saying that the higher you drop the ball, the higher it will bounce back, this is because at a height when you drop the ball, the GPE will be turned into kinetic energy (except for those lost to air resistance):
Mg h = ½MV2
And so, from this calculation, we see that if you increase the height dropped then speed will also increase as the ball will have had extra time to accelerate. In addition, the faster the ball hits a surface, then the higher the bounce from the surface will be. I believe that the ball will bounce to around 40%-45% of its original height, as I have predicted above, despite whatever height that the ball is dropped from. This is because I believe that the internal friction and the push of the floor will be constant and so will therefore be a percentage loss, in the bounce.
This can be characterised by the formula:
Mg = Mg
Therefore: = H2 / H1
The constant will be from 0-1, with 0 being a dead ball, and 1 being a perfect bounce from a perfect ball made from true elastic materials (i.e. the bounce will be the same as the height dropped from). A predicted graph of the ball bounce with height dropped is as follows:
Experimental techniques
I will do the experiment as shown with the equipments:
I will drop the tennis ball measured from the bottom of the tennis ball and accordingly I will measure the height bounced from the bottom of the tennis ball.
Preliminary results
As you can see, I have dropped the ball in 25cm intervals right up to 300cm, and I got 12 readings (see the graph). From these preliminary results, I have deduced that with these amounts of intervals, I can plot an accurate graph without too many readings. In addition, I will need to repeat the readings at least twice, so that I will have three readings for each interval and can average out any errors from experimental or operational errors. However it is clear from the graph, although it was starting to curve off at the end, that the terminal velocity point is far greater than the 3 metres that I have allowed myself for the experiment.
