physics meteor

Investigating the Relationship Between Impact Speed of a Meteor with the Diameter of its CraterHigh Level PhysicsFull InvestigationCandidate: Mert İNAN Instructor: Mine GÖKÇE ŞAHİN• T.E.D Ankara High School •2013-2014

1Mert 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.


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.


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)


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)


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.


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.


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.


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 Bal l (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 Bal l (grams) (±0.01)

Trial 1 Trial 2 Trial 3

6.00 1.70 14.00 1.30 1.40 1.2012.00 1.60 14.00 1.30 1.10 1.2018.00 1.60 14.00 1.20 1.10 1.1024.00 1.60 14.00 1.00 1.00 1.0030.00 1.50 14.00 1.00 0.90 0.9036.00 1.70 14.00 0.90 0.90 0.8042.00 1.70 14.00 0.80 0.80 0.8048.00 1.60 14.00 0.80 0.70 0.8054.00 1.60 14.00 0.80 0.70 0.7060.00 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 he igh t o f F l o u r Under the Crater (cm) (±0.03)

D e p t h of the Crater ( c m ) (±0.04)

Gravitational 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 he igh t o f F l o u r Under the Crater (cm) (±0.03)

D e p t h of the Crater ( c m ) (±0.04)

Gravitational 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) 10

=> [(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.


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

Dep

th o

f Cra

ter

(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

Ave

rage

Sp

eed

of B

all (

m/s

)

Depth of Crater (cm)


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.


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”

BIBLIOGRAPHY1. 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


http://surveying.wb.psu.edu/sur351/geoid/grava.htm

http://surveying.wb.psu.edu/sur351/geoid/grava.htm

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