Physics Meteor

Investigating the Relationship
Between Impact Speed of a Meteor
with the Diameter of its Crater
High Level Physics
Full Investigation
Candidate: Mert İNAN
Instructor: Mine GÖKÇE ŞAHİN• T.E.D Ankara High School •2013-2014
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Mert İNAN• T.E.D Ankara High School 2013-2014

INTRODUCTION
What is a Meteorite?
! “Meteorites are naturally occurring objects that originate in space and survive a fall to the
ground through Earth's atmosphere. Most are remnants of asteroids or possibly comets.” When a
meteor hits the surface of a planet or another celestial body it creates a crater.
Craters
! Generally, craters are
the reminders of meteorites.
They are created when a
m e t e o r i t e i m p a c t s a n d
explodes. They are round and
bowl-shaped because the
collision of the meteorite bursts
out the materials from the area
and sends them to nearby
terrain. Meteorites can also
disrupt the atmosphere and
send away water and minerals to
the outer space.
Calculation of Kinetic and Gravitational Potential Energy of a Meteorite
! “Gravitational potential energy is energy an object possesses because of its position in a
gravitational field. The most common use of gravitational potential energy is for an object near the surface
of the Earth where the gravitational acceleration can be assumed to be constant at about 9.8 m/
s2” [1].Meteorites obey only gravitational potential energy (PE) rules while they are far from the
impact body. However, when they start to move and get into the gravitational field of the celestial
collision body (CCB), they start to move with exceeding velocity because of the gravity that the
CBB possesses. With this increasing velocity, meteorites start to gain kinetic energy.
2
Figure 1: An artist’s impression of the impact of a meteorite.
©http://scienceblogs.com/startswithabang/2009/05/07/could-an-
asteroid-have-wiped-o/

This conversion of potential energy to kinetic energy (KE) causes the meteorite to gain more
velocity. Eventually, the meteor hits the CBB at the end, creating a crater which has the radius
that has a relationship with the KE and PE of meteorite. There is an equation that calculates the
diameter of the crater with relationship to the KE and PE of the meteorite ;
Where D is the diameter of the crater, Cf is the crater collapse factor, ρa is the density of the
meteorite and ρt is the density of the celestial body.
! In this experiment, it is intended to calculate and tabulate the effects of velocity, kinetic
energy and potential energy of a meteorite on the radius of the crater. This is done by imitating
the general situation of collision using flour in a container as the terrain of celestial collision
body and using a plastic ball to symbolize the meteorite. Plastic ball is thrown from different
heights to the flour and the radius of the crater is observed. This experiment needed rather a
simple equation than the above equation. Although the above equation makes precise
calculations, it calculates the diameter of the crater that shows the equation is once again
inappropriate for this experiment. Because of these reasons the equation of potential and kinetic
energies is used;
mgh = ½mv²
! Where m is the mass of the meteorite (the
plastic ball), g is the gravitational acceleration of the
celestial body (9.8 m/s2 for Earth), h is the distance
between celestial body and the meteorite (throwing
height of ball) and v is the velocity of the meteorite.
Observing this equation and making trials of different
throwing heights for the ball were the main principles
of this experiment.
3
Figure 2: Another example of this
experiment.
© California Standard Tests
[2]

Aim:
! Meteorite impacts are in some way our only understanding of astronomical events in our
Earth. In fact, studying these impacts increases the only connection with the outer space. This
connection is only understood when their physical properties are observed. In order to calculate
these properties their remnants, craters, help us by providing enough data like diameter and
velocity of the meteorite. This experiment help us understand the basic properties of these
meteorites by a simple example; throwing balls at a hight to a container that is full of flour.
Research Question:
! How does the releasing height of the ball -increasing 6 cm at each trial and starting from
6.0 cm to 60.0 cm- affect the impact velocity,measured by ms^-1, measured by observing the
crater radius caused by the collision on the flour in container and using the equation of energy
conservation at constant pressure and temperature?
Hypothesis:
When the throwing height of the ball increases, the gravitational potential energy (mgh)
of the ball at halt increases. When the ball is released the kinetic energy just before it collides
with the flour becomes greater than that of smaller heights. So, the overall velocity, kinetic
energy, potential energy and the radius of the crater increase as the throwing height increases.
Independent Variable:
•Throwing Heights of the Ball
Dependent Variables:
•Depth of the crater
Controlled Variables:
•Pressure of the laboratory (atm)
•Temperature of the laboratory (℃)
•Mass of the ball (grams)
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This variable will be calculated by the subtraction of the height of the
flour under the crater from the average flour height in the container. Error
propagation will be diminished by measuring the height with toothpick.
This variable will be measured by a 100 cm ruler with millimetric
divisions and error propogation will be prevented by not moving the
dropper off of the certain desired point.
These variables should be controlled because the may affect
the outcome of the experiment by producing systematic errors.
They are going to be controlled by: doing the experiment in the
same place, not changing the flour or the ball and staying away
from magnetic sources.

•Type of flour
•Length, width and height of the container (cm)
•Height of the flour inside the container(cm)
•Gravitational acceleration (m/s²)
•Lengths of the toothpicks (cm)
•Mass of the flour in the container (grams)
•Length of the ruler (cm)
•Volume of the ball (cm³)
•Radius of the ball (cm)
•Magnetic field of the laboratory (mT)
Apparatus & Materials:
•300 grams of plain wheat flour
•15 x 10 x 5 container
•A plastic ball with a radius of 1 cm
•50 mL tap water
•50 mL Erlenmeyer Flask
•20 toothpicks
•100 cm ruler
•CPO Science Gravity Drop Equipment Module (http://store.schoolspecialty.com/OA_HTML/
ibeCCtpItmDspRte.jsp?minisite=10020&item=47962&section=98768) (Figure 3.g)
•Vernier LabQuest 2 Data Logger (Figure 3.d)
•Vernier Barometer Probe (Figure 3.b)
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a
b
c
d
e
Figure 3: Images of used materials in this
experiment

•Vernier Magnetic Field Sensor (Figure 3.c)
•Notepad
•Pen
Method:
I. Take the 15 x 10 x 5 container and pour 300
grams of plain wheat flour into it.
II. Set CPO Science Gravity Drop Equipment Module near the container and set the height of
the clump of the dropper as 6 cm.
III. Put the plastic ball into the dropper hollow.
IV. Pour 50 mL tap water into the 50 mL Erlenmeyer Flask. Rinse a toothpick inside this flask
and stick the toothpick into the flour facing the pointy ends to the vertical axis of the
container, turn it 360 degrees around inside the flour to stick more flour and get it out. The
small flour particles will attach to the toothpick. Then, using the ruler measure the length of
the attached flour particles by beginning from the tip of the toothpick to the end of the
attached flour particle layer. This process will give the height of the flour. (Figure 5)
V.Open Vernier LabQuest 2
Data Logger and attach
Vernier Barometer Probe and Vernier Magnetic Field Sensor to it. Measure the
atmospheric pressure and magnetic field. Then write them down as controlled variables.
VI. Release the ball from the dropper and make the first crater, then make two other craters for
trials 2 & 3.
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Start measuring here Finish measuring here
ToothpickFlour
Figure 5: Sticking flour on the toothpick
Diameter
Radius
Figure 4: A general representation of the
diameter and the radius of the crater.

VII. Take different toothpicks and measure the height of the flour under the crater using the the
technique on the IV. step and note the results down.
VIII.To find the radius of the crater, subtract the height of the flour under the crater from the
normal height of the flour. (Figure 4)
1.65 - (Height of the Flour Underneath the Crater) = Radius of Crater
IX. Repeat the steps I to VIII ten times. However, change the throwing height of the ball
increasing constantly by 6 cm.
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Ball
Ruler
Flour
Craters of Trials 1 & 2
Figure 6: The schematic and general
model of this experiment.
Dropper
Toothpick

DATA COLLECTION AND PROCESSING
!
! After completing the design of the experiment and doing it, formed the following results
and after obtaining these results graphs also formed.
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Raw Data Table: This table shows the throwing height values and the height of the flour under the
crater values of ten different and constantly increasing heights with three trials.
H e i g h t o f t h e
Level of Thrown
Ball (cm) (±0.01)
Height of the
Flour in the
Container (cm)
(±0.01)
Mass of the
Ball (grams)
(±0.01)
Height of the Flour Under the Crater (cm) (± 0.01)Height of the Flour Under the Crater (cm) (± 0.01)Height of the Flour Under the Crater (cm) (± 0.01)
H e i g h t o f t h e
Level of Thrown
Ball (cm) (±0.01)
Height of the
Flour in the
Container (cm)
(±0.01)
Mass of the
Ball (grams)
(±0.01)
Trial 1 Trial 2 Trial 3
6.00 1.70 14.00 1.30 1.40 1.20
12.00 1.60 14.00 1.30 1.10 1.20
18.00 1.60 14.00 1.20 1.10 1.10
24.00 1.60 14.00 1.00 1.00 1.00
30.00 1.50 14.00 1.00 0.90 0.90
36.00 1.70 14.00 0.90 0.90 0.80
42.00 1.70 14.00 0.80 0.80 0.80
48.00 1.60 14.00 0.80 0.70 0.80
54.00 1.60 14.00 0.80 0.70 0.70
60.00 1.60 14.00 0.70 0.70 0.70
Height of the
L e v e l o f
Thrown Ball
(cm) (±0.01)
Height of the
Flour in the
C o n t a i n e r
(cm) (±0.01)
Height of the Flour Under
the Crater (cm) (± 0.01)
A v e r a g e
height of
F l o u r
Under the
Crater (cm)
(±0.03)
D e p t h
of the
Crater
( c m )
(±0.04)
Gravitation
al Potential
E n e r g y
( J o u l e s )
(±2%)
Average
S p e e d
o f t h e
Ball (m/
s) (0.01)
Height of the
L e v e l o f
Thrown Ball
(cm) (±0.01)
Height of the
Flour in the
C o n t a i n e r
(cm) (±0.01)
Trial 1 Trial 2 Trial 3
A v e r a g e
height of
F l o u r
Under the
Crater (cm)
(±0.03)
D e p t h
of the
Crater
( c m )
(±0.04)
Gravitation
al Potential
E n e r g y
( J o u l e s )
(±2%)
Average
S p e e d
o f t h e
Ball (m/
s) (0.01)
6.00 1.70 1.30 1.40 1.20 1.30 0.32 0.008 1.08
12.00 1.60 1.30 1.10 1.20 1.20 0.42 0.016 1.53
18.00 1.60 1.20 1.10 1.10 1.13 0.49 0.024 1.87
24.00 1.60 1.00 1.00 1.00 1.00 0.62 0.032 2.16
30.00 1.50 1.00 0.90 0.90 0.93 0.69 0.040 2.42
36.00 1.70 0.90 0.90 0.80 0.87 0.75 0.048 2.65
42.00 1.70 0.80 0.80 0.80 0.80 0.82 0.056 2.86
48.00 1.60 0.80 0.70 0.80 0.77 0.85 0.064 3.06
54.00 1.60 0.80 0.70 0.70 0.73 0.89 0.072 3.25
60.00 1.60 0.70 0.70 0.70 0.70 0.92 0.080 3.42
Table 2: This table shows the raw data tale values in addition with calculated values such as; average
height of the flour under the crater, depth of the crater, gravitational potential energy and average
speed of the ball. There are 10 increasing heights in each three trials.

Example Calculations:
•In order to find the radius of the crater of the 6 cm throwing height following formula is used;
1.65 - (Height of the Flour Underneath the Crater) = Radius of Crater
1.65 - [(1.30 + 1.40 + 1.20)/3] = 0.32 cm
•Using the kinetic and potential energy equation the velocity of the ball can be calculated for the
throwing height of the ball of 6 cm as;
mgh = ½mv²
14 grams x 9.8 m/s² x 0.06 metres = ½ x 14 grams x v²
v² = 2 x 9.8 x 0.06
v = √1.176
v ≃ 1.08 m/s
Sample Uncertainty Calculation:
[(Mean of Velocity Values) - Sample Velocity] / (Mean of Velocity Values)
Mean of Velocity Values = (1.08+1.53+1.87+2.16+2.42+2.65+2.86+3.06+3.25+3.42)
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=> [(2.43-1.08)/ 2.43] x 100 = 55.5 %
• As a result it is observed after 10 different heights that radius of the crater increases
when the velocity of the ball increases. However, as the graphs on the following page
show us, the increase rate of the radius of the crater starts to decrease as the throwing
heights increases, creating a parabolic graph.
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Graphs:
0.25
0.32
0.39
0.46
0.53
0.60
0.67
0.74
0.81
0.88
0.95
0 10.00 20.00 30.00 40.00 50.00 60.00
Depths of Craters at Different Throwing Heights
DepthofCrater(cm)
Throwing Heights (cm)
0.50
0.80
1.10
1.40
1.70
2.00
2.30
2.60
2.90
3.20
3.50
0.25 0.40 0.55 0.70 0.85 1.00
Depths of Craters in Relationship with Average Speed of Ball
AverageSpeedofBall(m/s)
Depth of Crater (cm)
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Graph 1: This graph shows the depths of the craters in 10 constantly increasing throwing
heights of ball for 3 trials. x-intercept and y-intercept error bars show the 0.01 cm difference
Graph 2: This graph shows the proportional relationship between the depths of the craters
and the average speed of ball. Two worst lines are drawn and the error bars for x and y
intercepts are drawn for the value of 0.01 cm.

CONCLUSION & EVALUATION
! This experiment has shown us the real relationship between the crater radius and the
velocity, thus the kinetic and potential energy of a meteorite. We found out this relationship by
using Potential and Kinetic Energy Equilibrium. Changing heights helped us to see the exact
change in the velocity of the meteorites. Graph 2 also represents this proportional relationship
with depth of a crater and the velocity of meteorite.
! When we look at Graph 1, we can see that the depths (radii) of craters are increasing
decreasingly. So this situation caused the graph to be a parabolic. This shows the indirect
relationship of depth of the craters with the heights.
! This experiment was only a representation of a big-scale impact of a meteorite and
formation of a crater. Looking at a real experiment with real meteorites and kilometers-wide
craters can boost our understanding of this experiment. David A. Kring made an observation of
Barringer Meteorite Impact Crater [3] and he measured and displayed the overall scenario of
collision with the help of graphs and schemes. One of his work includes Figure 7.
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Figure 7: David A. Kring’s creation of Barringer Crater profile

! In the Figure 7, the dissected part of a crater from a horizontal point of view is given. It
shows the altitude of the both ends of the crater and the pit. The total distance between edges of
the crater is also present, which may also show the diameter of the Barringer Meteorite. This
investigation is closely related to this experiment in the sense of the resemblance of the model of
observation: meteor craters. However, the Barringer Investigation is a much more big
experiment.!
When we look at Graph 1 we can see a parabolic curve. This means that there was another factor
that was affecting the radius of the crater; air friction. As this experiment wasn’t done in a
vacuumed chamber there was air friction involved in the decreasingly increasing values of the
radius. However, although this can be categorized as a systematic error, one can also observe the
same problem in the real situation; the real crater of a meteorite. Real meteorites are also affected
by the huge atmosphere of the Earth, if they can overcome this barrier they can collide with Earth
but with a smaller velocity than they had in the vacuumed space. As a result this error
propagation may be regarded as a normal consequence.
! The overall experiment can be finally summarized as an adequate and a virtual but
resemblant-to-the-real-meteorite model experiment that can be a good alternative to really grasp
the whole concept of collision.
! All in all, it can be said that the hypothesis was a correct one but with simple additions;
“So, the overall velocity, kinetic energy, potential energy and the radius of the crater increase as
the throwing height increases discarding the air friction of the atmosphere of Earth”
BIBLIOGRAPHY
1. Charles D. Ghilani (2006-11-28). "The Gravity Field of the Earth". The Physics Fact Book. Penn State
Surveying Engineering Program. Retrieved 2009-03-25
2. Vanissra Boonyaleepun, Se-Won Jang, “Formation of Craters in Sand”, ISB Journal of Physics, June 2007,
International School Bangkok
3. C. David Whiteman, Sebastian W. Hoch, and Maura Hahnenberger, Andreas Muschinski, Vincent Hohreiter,
Mario Behn, and Yonghun Cheon, Sharon Zhong and Wenqing Yao, David Fritts, Craig B. Clements, Thomas
W. Horst, William O. J. Brown, and Steven P. Oncley, “Metcrax 2006 Meteorological Experiments in
Arizona's Meteor Crater”, Bull. Amer. Meteor. Soc., 89, 1665–1680
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