Class Notes 4.18.11
Bouncing ball lab
is due
Bouncing ball lab .PE
Wednesday by
3pm.
Equation Sheet
Lab: Finding PE
(Mass)
Reading Notes:
Bouncing Ball Physics
Retake TEST by Thursday 4.21.11
Hw LATE -50%
Twin Towers worksheet Late -30%
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=345
Page 5 space # 3
CONDITIONS FOR USE:
Use to find the COR,
Or to predict how high
a resilient object will
rebound
• Coefficient of Restitution (ELASTICITY)
• Coefficient of Restitution
• Height bounce
e
no label
COR no label
hB
meters
• Height of the drop
hD
meters
Coefficient of Restitution
(COR)
• A COR of 1 would be a perfectly elastic
collision
• A COR of 0 would be a perfectly
inelastic collision.
COR
0≤ e ≤1
• We have dropped various balls and
found the Elastic Coefficient of
Restitution
Making restitution
return to the way it was
• IF someone
Takes $300 -- repay $300
100% restitution
• Shoplift and do community service
<100%restitution
Approximate coefficient of restitution for
different types of balls
type of ball
coefficient of restitution
Superball
0.9
Tennis ball
0.75
Baseball
0.55
Foam rubber ball
0.30
Beanbag
0.05
Calculate the Potential energy from the drop
height and the bounce height
page 5 space 4
Always
positive!
Bouncing Ball
• When the
bottom gets
flatter
• energy is
changed to
stored energy
in the bonds
of the ball
• by the bending
of the material
of the ball
A boulder resting at the top of a
hill has
potential energy.
• Gravitational
Potential
Energy is the
energy stored
due to height.
• Work can
change the
height of the
Boulder
• Work can
change the
potential
energy of the
Boulder
We Graphed all three points, but
Average the three trials for PE
Drop Height
20
40
60
80
100
120
140
160
Bounce #1
Height
Bounce #2 Height Bounce #3
Height
Average
Bounce height
H20
H40
H60
H80
H100
H120
H140
H160
Use the average height for PE
Drop
Height
hD (cm)
20
40
60
80
100
120
140
160
Average
Bounce
Height hB
(cm)
Drop
PED=mghD
Bounce
PEcB=mghB
Δ PE
(PEB-PED)
Use the Masser to find the mass in
grams
• Be sure to use the same tray of spheres.
• There is only one masser, so please work
carefully and quickly.
• Be sure the spheres are in the same tray
when you finish.
Mass of bouncing ball
Then find PE: in kg and meters
• Find the mass on the balance (take turns)
Record the mass in grams on the data table
• Convert the mass to kg ( divide by 1000)
• EX:
35.7 g = .037 kg
• Convert the height to m (divide by 100)
• Calculate the PE for the original height (in
meters) and the first bounce and record it on
the data table you may use 10 m/s/s for the ag
in the equation :
PE = mgh
A bouncing basketball captured with a stroboscopic flash at 25
images per second. Ignoring air resistance, the square root of the
ratio of the height of one bounce to that of the preceding bounce
gives the coefficient of restitution for the ball/surface impact.
Potential energy changes to kinetic
energy due to work done by gravity
PE
Bouncing of ball
• If a soccer ball is dropped on
a hard surface, it will bounce
back to a height lower than
its initial position. Such kind
of motion is called the
bouncing of the soccer ball,
which plays an important role
in the motion of the ball. Let
us study the mechanism of
the bouncing of the ball in
• The relative
details.
bounciness of different
types of balls
• The coefficient of restitution is how you
quantify bounciness or give bounciness a
number, and you do that by dividing the
bounce height by the drop height, then
finding the square root of that. When...
Read more:
http://wiki.answers.com/Q/What_is_the_C
oefficient_of_Restitution_of_bouncing_a_b
asketball#ixzz1JW73FiKE
• As a result, a ball with smaller coefficient of
restitution rebounds to lower height in
successive bounces and a shorter time is
required for the ball to stop (see below figure).
For example, grass reduces the coefficient of
restitution of a soccer ball since the bending of
blades causes further loss of its kinetic energy.
Therefore, it would take a shorter time for the
soccer ball to stop if it is kicked on grass instead
of hard floor.
The Total Mechanical Energy
• As already mentioned, the mechanical energy
of an object can be the result of its motion (i.e.,
kinetic energy) and/or the result of its stored
energy of position (i.e., potential energy). The
total amount of mechanical energy is merely the
sum of the potential energy and the kinetic
energy. This sum is simply referred to as the
total mechanical energy (abbreviated TME).
• TME = PE + KE
• As discussed earlier, there are two forms of
potential energy discussed in our course gravitational potential energy and elastic
Mechanical Energy as the Ability
to Do Work
changing its temperature.
• We can also change the bounciness of a ball by changing its
temperature. Take two baseballs that bounce to about the same
height. Put one in the freezer for an hour and leave the other at
room temperature. Then compare their bounciness again. You
should notice that the room temperature ball bounces a little bit
higher. The cold ball would bounce about 80 percent as high as the
room temperature ball. Although the difference of bounciness is not
dramatic, it's enough to see that temperature can be a factor: it
could make the difference between a home run and a pop fly.
• However, the change in bounciness due to the change in
temperature is taken for granted for some sport. For example,
squash player rely on the pre-game warm up to warm up the ball as
well as the players.
Surface bounced on
• Example…grass reduces the coefficient of
restitution of a soccer ball since the
bending of blades causes further loss of its
kinetic energy. Therefore, it would take a
shorter time for the soccer ball to stop if it
is kicked on grass instead of hard floor.
• Coefficient of restitution of a tennis ball is
0.712. Thanks ...
•
1910 soccer ball [ii]
1950 soccer ball [ii]
2004 Euro Cup ball [ii]
•
In the late 1980s, the leather casing ball was replaced by totally synthetic ball in soccer
competitions. The covering material of the totally synthetic ball is synthetic leather made from
polymer. For high quality ball, the casing is made of the synthetic leather panels stitched together
through pre-punched holes by waxed threads. The bladder of a totally synthetic ball is usually
1910
ball [ii]The ball is then
1950
soccer
ball [ii]
2004through
EuroaCup
ball [ii]
latexsoccer
or butyl bladder.
inflated
by pumping
air into its bladder
tiny hole
on the casing. The totally synthetic ball could resist water absorption and reliably maintain its
shape.
•
The Internal structure of a totally synthetic soccer ball [ii]
•
Nowadays, the official soccer rules called the "Laws of the game", which are maintained by the
International Football Association Board (IFAB), specify the qualities of the ball used in soccer
matches. According to the laws, the soccer ball should satisfy the following descriptions:
•
it is spherical in shape,
•
its casing is made of either leather or other suitable material,
•
its circumference is not more than 70 cm and not less than 68 cm,
•
its weight is not more than 450 g and not less than 410 g at the start of the match.
•
its pressure inside equal to 0.6 - 1.1 atmosphere at sea level.
Figure explaining the extra
pressure inside the soccer ball.
The relative bounciness of
different types of balls [iii]
• Energy change in the falling ball after release
until hitting on the ground.
(Note that here "G.P.E." and "K.E." stand for the
gravitational potential energy and kinetic energy
respectively.)
Work must be done in order to
distort an elastic object
•
. Therefore, if you pull a spring outward so that it become longer, some
energy must have been transferred from yourself to the spring. The energy
stored in an distorted object due to its deformation is called the elastic
potential energy. So, when talking about the elasticity of the ball, we are
indeed talking about the spring-like behavior of the ball. In other words, we
are considering the tendency of the ball to return to its original spherical
shape when it is being squeezed. Where does the elasticity of the ball come
from? The elasticity of a solid ball arises from the elasticity of the
constituting material which is due to the interatomic or intermolecular force
inside. In contrast, for air-filled ball like soccer ball, its elasticity is resulted
from the extra air pressure inside the ball. What happens to a ball after you
dropped it above a hard floor? The gravity pulls the ball toward the ground
and thus the ball falls leading to the lost of its gravitational potential energy.
By the law of conservation of energy, the ball must gain kinetic energy and
so it falls towards the ground with an increasing speed. Subsequently, the
ball hits the hard floor with a high speed. (Note that the ball always moves
with the downward acceleration of g = 9.8 m/s2 as it falls.)
The elasticity of an object
means
• the tendency of the object to return to its equilibrium shape, the
natural shape of the object with no net force applied on it, when it is
being deformed. And the force for the object to restore to its
equilibrium shape is called the restoring force, which is always
directed in opposite to the deformation of the object. Almost all real
rigid body are elastic, i. e. having certain extent of elasticity. A trivial
example of an elastic object is the spring. You probably have the
experience that a spring would tend to restore to its original size
when you stretch it to be longer. Scientist found that, providing the
deformation is not too large, the relationship between the distortion
and the restoring force is given by the Hooke's law:
"The restoring force exerted by an elastic object is proportional to
how far it has been distorted from its equilibrium shape."
The restoring force Fs on a spring in case of different extension.
Law of conservation of energy
•
In the law of conservation of energy, it was stated that:
"Energy can neither be created or destroyed but can only be changed from one form
to another."
Therefore, the amount of total energy in an isolated system must be constant. For
example, let us consider a piece of charcoal placed in an isolated room. If we burn
the charcoal, the chemical energy inside the charcoal is changed into the thermal
energy of the room. Then the temperature inside the room would be increased.
When the ball hits the ground, the ball exerts force on it. By the Newton's 3rd law of
motion, the ground exerts a force on the ball as well. The motion of the ball would be
stopped by the (stationary) hard floor resulting in the compression of the ball. So the
work done on the ball leads to the increase of the elastic potential energy of the ball.
That means some of the kinetic energy of the ball (which is converted from the
gravitational potential energy of the ball) is converted into the elastic potential energy
when the ball hits the ground. On the other hand, some of the kinetic energy is lost as
thermal energy during the impact due to either the internal friction of the ball or the
heating of the surface.
•
Energy change in the falling ball during the impact
After losing all the kinetic energy,
the ball becomes momentarily at
rest.
• The squashed ball would simply act like a compressed spring. The
ball pushes the ground with a restoring force proportional to its
displacement from the equilibrium position (Hooke's law). In
consequence, the ground pushes back the ball with a force of equal
magnitude but opposite in direction. Thus the ball bounces back in
upward direction. During the rebound, the stored elastic potential
energy is released as the kinetic energy of the ball which is then
converted to gravitational potential energy as the ball moves up.
Moreover, some of the elastic potential energy is lost again due to
friction or heat which results in slight heating of the ball. The ball
keeps on going upward until it comes to rest after losing all its kinetic
energy again. Due to the lost of some of the initial gravitational
potential energy into thermal energy, the ball cannot bounce back to
the original height.
What is the
Coefficient of Restitution?
(also called: Elastic Coefficient)
What is the slope of each of the graphs?
• Use the slope of the graphs to find the
Coefficient of Restitution, just like we did for
the Spring Constant.
• The Coefficient of Restitution tells us how
“springy” the ball is.
• The slope of the graph represents this
constant. The constant will be the same for a
given ball.
PE Bouncing Ball Lab
Work and Potential Energy and Problems
Patterns in graphs
Increasing/decreasing/ no change
Linear or curved line of best fit.
Bouncing ball lab
measure height at the first bounce up
and the second bounce
Work to PE
or PE to work
• a force acts upon it
and
changes the height
Measurement of Horsepower
• The maximum horsepower
developed by a human being over
a few seconds time can be
measured by timing a volunteer
running up the stairs in the lecture
hall.
• If a person of weight W runs up
height h in time t, then h.p. = Wh/t
X 1/550 ft-lbs/sec.
• A person in good shape can
develop one to two horsepower. It
will be entertaining to the students
if the professor tries it too.
• Should the person be allowed a
running start?
http://www.physics.ucla.edu/demoweb/demomanual/mechanics/energy/faith_in_physics_pendulum.html
Bouncing Ball
Bouncing a Ball
•
•
•
•
What you need:
a tennis ball
a basketball
a room without breakables
• Instructions:
Drop the tennis ball from waist height and see how high it bounces.
Drop the basketball from the same height and see how high it bounces.
Put the tennis ball on top of the basketball and drop them both at arms
length from waist height.
• Results & Explanation:
The tennis ball should bounce a lot higher than before. When the balls hit
the ground, momentum from the basketball was transferred to the tennis
ball making it go much higher than before.