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IA for IB curriculum, grade 7 awarded, in depth analysis, marked against 2021 IB rubric, structured
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Effect of temperature on the coefficient of restitution of sports ballsCandidate Code: jbd581
1
, How does temperature affect the coefficient of restitution of various sports balls?
1 Introduction
One of the most viewed sports events is the FIFA World Cup, attracting people of all ages, all
over the globe. The next FIFA World Cup is taking place in Qatar in 2022, one of the hottest
countries in the world, where temperatures get up to 43℃ in the summer. This got me
thinking about the effect temperature will have on the behaviour of a football. It has been
proven that there is a relationship between temperature and the elasticity of a collision. 1
The dynamic behaviour of balls upon impact with a surface plays an important role in
numerous sports. This interaction is measured using a ratio called the coefficient of
restitution and determines the elasticity of a collision.
As sport is a fundamental aspect of my life, I thought this would be an interesting IA
investigation that would allow me to apply my theoretical knowledge from physics to a
great passion of mine in the real world. Upon further research I realized that there are
multiple factors that affect the coefficient of restitution, one being temperature. Intrigued
by this concept, I thought it would be an ideal topic to investigate. Having learned about the
different energy conversions that occur when a ball is dropped and the losses of energy due
to inelastic collisions that result in a lower rebound height, it led me to the following
research question How does temperature affect the coefficient of restitution of various
sports balls?
2 Aim
In this IA, I will investigate the effect of temperature on the coefficient of restitution (COR)
on tennis, rounders, footballs and ping pong balls. I hope to find a correlation between the
two variables and thus determine the optimal temperature which produces the highest
rebound height for each ball. Through this experiment, I will determine which of the four
balls has the highest coefficient of restitution.
3 Hypothesis
The higher the temperature, the higher the rebound height and thus the higher the
coefficient of restitution. As the temperatures increases, the pressure inside the ball will
increase because the particles within the ball will hit against the walls more frequently. I
1
“Queensland Parliament.” Accessed March 1, 2021.
https://www.parliament.qld.gov.au/documents/committees/EIC/2013/QldAssessment/tp-20Mar2013-
Assignment.pdf.
2
, think the correlation between temperature and coefficient of restitution will be inversely
exponential.
4 Background Information
4.1 Energy Transformations
When a ball is dropped, a series of energy conversions occur. Initially, a ball at a given height
will possess gravitational potential energy and no kinetic energy. As it falls, some of this
energy is transformed into kinetic energy because it is in motion and this gradually increases
as the ball gains momentum, until it collides with the surface. Just before the ball hits the
ground, its gravitational potential energy will be 0, because G.P.E is dependent on height
(which will be 0), and the kinetic energy is at its maximum. During the collision, the ball
deforms and the K.E is transformed into elastic potential. As no ball can be perfectly elastic,
the energy is not completely converted and in turn some of the energy is lost to sound and
heat. As the ball rebounds, the elastic potential is converted back into K.E and then G.P.E as
it rises. The ball’s maximum rebound height will be lower than the initial drop height as
some energy has been lost to the surroundings during the collision. 2 The ratio between the
initial and rebound height is analysed using the coefficient of restitution.
4.2 Coefficient of Restitution
The coefficient of restitution (COR) usually ranges from 0-1.3 A COR value of 1 means a
perfectly elastic collision, and a COR value of 0 means a perfectly inelastic or plastic
collision, the ball will not bounce at all after the collision. It is a good way to specify how
much kinetic energy is lost to surroundings. The COR can be calculated by either finding the
ratio of the initial to final velocity, or the ratio between the initial and final rebound height.
As a preliminary study, I tried both techniques, on each of the selected ball types, to see
which resulted in the most accurate data. Due to the high uncertainty in the available
equipment to measure the velocity of the ball, I decided to measure the rebound height of
the ball.
ℎ(
𝑒=&
ℎ)
2
Mini Physics. “Case Study 2: Energy Conversion for A Bouncing Ball.” Mini Physics, January 19, 2020.
https://www.miniphysics.com/case-study-2-energy-conversion-for-a-bouncing-ball.html.
3
Weir, Graham, and Stephen Tallon. “The Coefficient of Restitution for Normal Incident, Low Velocity Particle
Impacts.” Chemical Engineering Science. Pergamon, April 7, 2005.
https://www.sciencedirect.com/science/article/pii/S0009250905001508.
3
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