International Baccalaureate Physics Higher Level Internal Assessment
Personal code: hlt648 Session: May 2020
Topic: Bouncing ball's dependency on its temperature
Declaration: I declare that this work is my own work and is the final version. I have acknowledged
each use of the words or ideas of another person, whether written, oral or visual.
1. Rationale for the research
Ever since the primary school, I have been engaged in numerous sport activities in which
balls of different types are in use. The one I found the most interesting and fascinating was
table tennis. I would spend every afternoon training this sport in a sport Club, and every
second of my leisure time playing it with my father outside my block of flats, on communal
tables. Having become more professional, I started noticing how significantly my skills
differed when playing casually outside, compared to the dedicated space during trainings
and tournaments. I used to wonder what contributed to this dispersion and yet I am writing
this lab report to find out if one of my hypotheses - the temperature affects the behaviour of
the ball - was true, which would have explained many of my past deliberations.
2. Background research and information
The topic of bouncing balls of various nature has been investigated by various physicists for a
long time, especially in the era of countless sports featuring various balls. Usually, when
talking about the ball's bounce and its properties, it is assumed that the ball is released from
a rational and achievable height, without any initial velocity, and is later on incident on a
uniform surface. The ball's initial energy is given by:
where 'Ep' is its potential energy, 'm' is its mass, 'g' is the gravitational acceleration,
standardly approximated to 9.81 [ms-2], and 'h0' is its initial height.
Right before the ball hits the surface, its entire potential energy is already transformed, so
that the system's energy is preserved, into kinetic energy which is given by:
1
, Where 'Ek' is its kinetic energy, 'm' is its mass, and 'v' is its current velocity.
As the ball hits the surface, it experiences a collision, after which it rebounds back to some
height 'h1'. Should this collision be perfectly elastic, there would be no energy loss and 'h1'
would equal 'h0'. Nonetheless, despite the collisions amongst the subatomic particles, all real
world collisions are inelastic. (Texasgateway.org, 2019) This means following the collision
some energy is lost to the environment, in the case of a bouncing ball - in the form of heat
and sound, the kinetic energy of the ball is transferred to elastic potential energy for a brief
moment, and after the rebound it is transferred back to the kinetic energy. Consequently,
the ball's 'Ek' after hitting the surface decreases. The ball's velocity after the impact may be
given by manipulating the previous formula:
| | √
where 'vi' is the ball's velocity right after the impact, 'Ek1' is its kinetic energy right after the
impact, and 'm' is its mass. The expression is negative, as the velocity is directed in the
opposite direction relative to the initial height. Equating the energy in the system:
where 'm' is the ball's mass, 'h1' is its height after the rebound, 'vi' is its velocity right after
the rebound, and 'g' is the gravitational acceleration, the formula for 'h1' may be derived:
where 'h1' is the ball's height after the rebound, 'vi' is its velocity right after the rebound, and
'g' is the gravitational acceleration.
This leads to a conclusion that 'h1' after the rebound varies due to the collision's inelasticity
as well. The proportion of the ball's velocity after the impact to the ball's velocity right
before the impact is called its 'bounciness' or 'coefficient of restitution (COR).' (Madden,
2011) Alternatively, COR may be measured as the proportion of the square root of the ball's
maximum height after the rebound to the square root of the ball's initial height. For a
perfectly elastic collision the COR would equal 1.
2
Personal code: hlt648 Session: May 2020
Topic: Bouncing ball's dependency on its temperature
Declaration: I declare that this work is my own work and is the final version. I have acknowledged
each use of the words or ideas of another person, whether written, oral or visual.
1. Rationale for the research
Ever since the primary school, I have been engaged in numerous sport activities in which
balls of different types are in use. The one I found the most interesting and fascinating was
table tennis. I would spend every afternoon training this sport in a sport Club, and every
second of my leisure time playing it with my father outside my block of flats, on communal
tables. Having become more professional, I started noticing how significantly my skills
differed when playing casually outside, compared to the dedicated space during trainings
and tournaments. I used to wonder what contributed to this dispersion and yet I am writing
this lab report to find out if one of my hypotheses - the temperature affects the behaviour of
the ball - was true, which would have explained many of my past deliberations.
2. Background research and information
The topic of bouncing balls of various nature has been investigated by various physicists for a
long time, especially in the era of countless sports featuring various balls. Usually, when
talking about the ball's bounce and its properties, it is assumed that the ball is released from
a rational and achievable height, without any initial velocity, and is later on incident on a
uniform surface. The ball's initial energy is given by:
where 'Ep' is its potential energy, 'm' is its mass, 'g' is the gravitational acceleration,
standardly approximated to 9.81 [ms-2], and 'h0' is its initial height.
Right before the ball hits the surface, its entire potential energy is already transformed, so
that the system's energy is preserved, into kinetic energy which is given by:
1
, Where 'Ek' is its kinetic energy, 'm' is its mass, and 'v' is its current velocity.
As the ball hits the surface, it experiences a collision, after which it rebounds back to some
height 'h1'. Should this collision be perfectly elastic, there would be no energy loss and 'h1'
would equal 'h0'. Nonetheless, despite the collisions amongst the subatomic particles, all real
world collisions are inelastic. (Texasgateway.org, 2019) This means following the collision
some energy is lost to the environment, in the case of a bouncing ball - in the form of heat
and sound, the kinetic energy of the ball is transferred to elastic potential energy for a brief
moment, and after the rebound it is transferred back to the kinetic energy. Consequently,
the ball's 'Ek' after hitting the surface decreases. The ball's velocity after the impact may be
given by manipulating the previous formula:
| | √
where 'vi' is the ball's velocity right after the impact, 'Ek1' is its kinetic energy right after the
impact, and 'm' is its mass. The expression is negative, as the velocity is directed in the
opposite direction relative to the initial height. Equating the energy in the system:
where 'm' is the ball's mass, 'h1' is its height after the rebound, 'vi' is its velocity right after
the rebound, and 'g' is the gravitational acceleration, the formula for 'h1' may be derived:
where 'h1' is the ball's height after the rebound, 'vi' is its velocity right after the rebound, and
'g' is the gravitational acceleration.
This leads to a conclusion that 'h1' after the rebound varies due to the collision's inelasticity
as well. The proportion of the ball's velocity after the impact to the ball's velocity right
before the impact is called its 'bounciness' or 'coefficient of restitution (COR).' (Madden,
2011) Alternatively, COR may be measured as the proportion of the square root of the ball's
maximum height after the rebound to the square root of the ball's initial height. For a
perfectly elastic collision the COR would equal 1.
2
