1. The effects of age on the energy lost in the bounce of a tennis ball
Neal Doolin

2. Bouncing Physics 𝑃𝐸=𝑚𝑎𝑠𝑠 ∗𝑔𝑟𝑎𝑣𝑖𝑡𝑦 ∗ℎ𝑒𝑖𝑔ℎ𝑡 𝐾𝐸= 1 2 ∗𝑚𝑎𝑠𝑠 ∗𝑣𝑒𝑙𝑜𝑐𝑖𝑡 𝑦 2
In conservative system, energy is conserved in this interaction – none would be lost in the bounce:
𝑃𝐸 + 𝐾𝐸 = 𝑃𝐸 + 𝐾𝐸

3. Background and Objective
Tennis balls are sold in pressurized cans because their core has a set pressure above the atmosphere’s.
Objective: Find the effects of age (time since depressurization) on the energy lost in the bounce of a tennis ball.
In other words, how much higher does a new ball bounce than an old one?

4. Bouncing Physics cont’d
The real world is non-conservative. Energy is lost to air resistance and in the compression of the ball during the bounce.
At the height of a bounce, there is no KE. This allows the interaction to be simplified to
𝑃 𝐸 𝑖 = 𝑃 𝐸 𝑓 + 𝑊
Finding W is rather useless; describing the relationship between 𝑃 𝐸 𝑖 and 𝑃 𝐸 𝑓 provides a more complete picture. Since gravity and the balls’ masses won’t change, I only need measure initial and final heights.

5. Methods
A tennis ball was dropped in such a way that it was always in frame of the camera and did not move towards or away from the camera
On average, recorded 6 bounces per trial
Used Tracker to mark the ball at its highest points.
One bounce’s rebound height becomes the next bounce’s initial height.
Recorded over a period of 27 days after opening the can
Track Coefficient of Restitution: ℎ𝑒𝑖𝑔ℎ 𝑡 𝑟𝑒𝑏𝑜𝑢𝑛𝑑 ℎ𝑒𝑖𝑔ℎ 𝑡 𝑖𝑛𝑖𝑡𝑖𝑎𝑙

6. Results

7. Results Cont’d – Ball 3 Exponential Fit – 1 Year
Exponential Fit – 2 Years
The CoR was expected to exponentially decay; however, fitting the data provided a very low 𝜒 2 value, plus the results do not make sense.

8. Conclusion and Discussion
The restitution coefficient of a tennis ball decreases after being depressurized – a ball loses a larger percent of its initial energy in a bounce after aging.
Still expect an exponential or power result
Sources of error:
Systemic: ~2cm on the meter stick, 2cm (pixilation)
Statistical: Low sample size, large standard error
A significantly larger sample size is necessary to determine to more accurately discuss the aging affects of tennis balls

9. Modeling Can model ball bouncing as ℎ 𝑓 = ℎ 𝑖 ∗𝐶𝑜 𝑅 𝑛
Where 𝑖 is the initial height, 𝑓 the final, and 𝑛 is the bounce number.
Energy lost : 𝐸=𝐶𝑜𝑅 ∗ ℎ 𝑖
Total Energy Lost in 𝑛 bounces:
𝐸 𝑡𝑜𝑡 = ℎ 𝑖 ∗ Σ 𝑗=1 𝑛 ( 𝑐 𝑗 )

10. Acknowledgements
Brad Williamson
Tim Dorn
Gavin Howard