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

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

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?

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.

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

Results

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.

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

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 )

Acknowledgements Brad Williamson Tim Dorn Gavin Howard