1. PHYSICS INVESTIGATION
“ANALYSING THE EFFECT OF MASS
OF THE OBJECT TO THE DEPTH OF
CRATER THAT THE OBJECT DID”
FULL INVESTIGATON
Ertuğrul AKAY
TED ANKARA COLLEGE
Instructor: Mine Gökçe ŞAHİN
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2. PART 1, DESIGN:
Research Question :
How does the change in depth of the crater made by the
impact force of a 2.7 gram table tennis ball which is dropped
from a distance 1 meter occur if the mass of the table tennis
ball increases by injection of 2 grams of water depends on
number of trials in a constant temperature , ground, density of
water added ?
Hypothesis :
The depth of the crater made by the impact force of a 2.7
gram table tennis ball which is dropped from a distance 1 meter
increases if the mass of the table tennis ball increases by
injection of 2 grams of water depends on number of trials in a
constant temperature , ground, density of water added .
Explanation:
The impact force of an falling object is equal to :
(½ .m.V2
)/d=Fav
*
m=mass of the object (gr)
V=Velocity (m/s)
Fav = Impact force
d=Distance (the height in this experiment , meter)
2
3. In this experiment d is constant.
Also, we can find V value by using this formula
m.g.h = (½ .m.V2
)
(PE)= (KE)
PE=Potential energy at 1 meter , at start.
KE=Kinetic energy when the object hit the ground.
Due to these formulas , we can say that mass is proportional
with Kinetic Energy , by the way impact force .
In an increase of mass increases the impact force so that the
object plunges into ground more and depth of the crater
increases.
*http://www.livephysics.com/tools/mechanics-tools/solve-problem-related-impact-force-falling-object/
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4. Variables:
Manipulated Variables :
1.The mass of the water for increasing the mass of table tennis
ball. (gr)
2.Falling time of the table tennis ball. (sec)
Controlled variables :
1. Mass of the table tennis ball. (cm3
)
2. Class of the ground (kg, flour)
3. Object (table tennis ball ) height from the ground (m)
4. Temperature of the system (C°)
5. Density of the water added into table tennis ball (kg/dm3
)
6. Width & depth of the ground (cm)
Responding Variables:
1.Depth of the crater (cm)
2.Impact force of the table tennis ball (N)
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5. Materials:
24 cm Saucepan (http://direct.asda.com/ASDA-Stainless-Steel-24cm-
Stockpot/001414176,default,pd.html?cgid=203114)
1 kg white flour (http://www.shipton-mill.com/flour-direct-shop/white-
flour)
A wooden 1 meter ruler (http://www.priceme.co.nz/Warwick-RULER-
WOODEN-1-METRE/p-885992073.aspx)
1 toothpick (http://www.utilitysafeguard.com/toothpicks)
1 injection shot (http://www.amazon.com/Present-Time-Silly-Injection-
Needle/dp/B0085X8ZF6/ref=sr_1_12?ie=UTF8&qid=1360116675&sr=8-
12&keywords=injection+shot)
20 gram tap water
A thermometer
Safety:
Be careful when using the injection shot .
Method/Procedure:
Note : Each throwing will repeated 5 times.(5x5)
Note: Be careful with the controlled variables for experiment.
1.Pour 1 kg flour in saucepan and flatten it.
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6. 2.Measure the depth of flour and note .
3.Place the ruler in saucepan but be careful not to change the
depth of flour and its smoothness. Also evaluate the
temperature and note .
4.Drop the table tennis ball from a 1 meter height.
5.Take the ball away and wet the toothpick to measure the
depth of crater.
6.Put the toothpick into the crater deeply and measure the
height buy looking the flour on the toothpick.
7. Subtract the flour toothpick height value from the normal
depth value and note .
8. Inject 2 grams of water by using injector shot (Be careful
while using this.) into the table tennis ball .
9.Do step 4 ,5,6,7 again for new mass of ball.
10.Inject 2 grams of water by using injector shot into the table
tennis ball.(It becomes 4 grams of water in the ball)
11 Do step 4 ,5,6,7 again for new mass of ball.
12.Inject 2 grams of water by using injector shot into the table
tennis ball.(It becomes 6 grams of water in the ball)
13.Do step 4 ,5,6,7 again for new mass of ball.
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7. 14. Inject 2 grams of water by using injector shot into the
table tennis ball.(It becomes 8 grams of water in the ball)
15.Do step 4 ,5,6,7 again for new mass of ball.
16.Clean all the materials and make a raw data table.
Figure 1 , Diagram of the experiment:
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8. PART 2 , DATA COLLECTION & PROCESSING:
Raw Data Table :
Trials mass of the table tennis ball
(g,±0.1)
mass of water added
(g,±0.1)
total mass
(g,±0.2)
Crater depth(cm,±0.5)
(For 5 trials ,each of them 1 trial)
1 2,7 0 2,70 0,51 0,45 0,52 0,46 0,53
2 2,7 2 4,70 1,00 1,05 1,01 0,9 1,02
3 2,7 4 6,70 1,29 1,24 1,32 1,28 1,28
4 2,7 6 8,70 1,52 1,55 1,53 1,51 1,53
5 2,7 8 10,70 1,62 1,63 1,66 1,66 1,64
Table 1.a : This table shows the mass of table tennis ball ,
mass of water added into ball , total mass of ball and water
and the crater depth arisen.
To find arithmetic mean:
Example , Trial 1 :
0.51+0.45+0.52+0.46+0.53=2.47±(0.1x5)
2.47±0.5 / 5= 0.49 ± (%20)
And to change the cm to meter :
(0.0049x20)/100
=0.005±0.001
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9. Table 2.a: This table shows the mean value of crater depth
with unit of meter, mass of the table tennis ball, mass of the
water added & total mass with unit of kilogram. And lastly,
height of the start .
To make a straight graph , we can take root of total mass :
Example ,Trial 1 :
(0.003)=0.06
(0.0002/0.003 )x100 = ± %7 x 2=%14
(0.055x14)/100=0.01
0.055 ±0.008
Trials Mass of the
table tennis
ball
(kg,±0.0001)
Mass of
water
added
(kg,±0.0001)
Total mass
(kg,±0.0002)
Mean of
crater depth
(meter)
Uncertainties
of crater
depth
(meter)
Height of the
start
(meter)
(±0.1)
1 0.003 0.000 0.003 0.005 0.001 1
2 0.003 0.002 0.005 0.010 0.001 1
3 0.003 0.004 0.007 0.013 0.001 1
4 0.003 0.006 0.009 0.015 0.001 1
5 0.003 0.008 0.011 0.016 0.001 1
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10. Table 3.a:This table shows the mean value of crater depth
with unit of meter, mass of the table tennis ball, mass of the
water added & total mass with unit of kilogram, height of the
start and root of total mass with uncertainties for all .
Trials Mass of the
table tennis
ball
(kg,±0.0001)
Mass of
water added
(kg,±0.0001)
Total
mass
(kg)
(0.0002)
Root
of
total
mass
(kg)
Uncertainties
of root of
total mass
(kg)
Mean
of
crater
depth
(meter)
Uncertainties
of crater
depth
(meter)
Height
of the
start
(meter)
(±0.1)
1 0.003 0.000 0.003 0.055 0.008 0.005 0.001 1
2 0.003 0.002 0.005 0.071 0.006 0.010 0.001 1
3 0.003 0.004 0.007 0.083 0.005 0.013 0.001 1
4 0.003 0.006 0.009 0.095 0.004 0.015 0.001 1
5 0.003 0.008 0.011 0.105 0.004 0.016 0.001 1
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11. Graph X.a : This graph shows the linear fit and best & worse
lines of depth of crater per root of total mass of table tennis
ball with uncertainties.
Note:To make the uncertainties different , I used another (z)
column for uncertainties of root of total mass of table tennis
ball .
Finding the impact force & velocity of the object:
PE =KE
Initial potential energy(PE) is equal to final kinetic energy (KE)
m.g.h=1/2.m.v^2
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12. m=mass of the object (kg)
g=gravitational force (m/s^2)
h=height (m)
v=velocity (m/s)
so that impact velocity is equal to �2. 𝑔𝑔. ℎ
In conclusion all trials have a velocity of √2𝑥𝑥9.81𝑥𝑥1
=4.43 m/s
Impact force is equal to
KE/depth of crater
Trial 1 :
[1/2x0.003x(4.43)2
]/0.005=9.81
5.88 ± (%20+7)
5.88 ± 2.65 N
Trial 2 :
[1/2x0.005x(4.43)2
]/0.010=
4.9 ± (%10+4)
4.90 ± 0.69 N
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14. Graph Z.X: This graph shows the linear fit and worst line(max. slope)
for impact force per total mass of table tennis ball .(There is no
other best & worst line for this graph because of the biggest trial 1
uncertainty.)
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15. PART 3 , CONCLUSION & EVAULATION:
The aim of the experiment is finding the impact force depends on
mass of the table tennis ball and height from the ground to make a
relationship between the crater depth made by ball and its mass. So
that, after the data collection I make two straight graph , one for
mass of ball-crater depth & mass of ball-impact force of the ball.
The result proves my hypothesis briefly “The depth of the crater
made by the impact force of a table tennis ball which is dropped from
1 meter increases if the mass of the table tennis ball increases.” We
can conclude this result by the graphs , mass of ball & crater depth ,
mass of ball & impact force of the ball are proportional each other.
There is only 1 big uncertainty for the experiment , trial 1 , on the
other hand this big uncertainty doesn’t change the conclusion and the
other values are mostly reliable.
There was a systematic error , air friction, which slows the speed of
the object (ball) so it decreases the impact force existed on the ground
also depth of crater. Also, there is another random error, the smooth-
ness of the ground. Despite we try to clear the crater and make the
ground same as beginning we cannot manage it perfectly so that the s
moothness of the ground changed therefore the next values of crater
depth changed.
To minimize the uncertainty , the air friction can be eliminated by
vacuuming the system . Moreover , the ground can change to an
orthopedic pillow which is able to from itself same as in the beginning
after a force existed on it.
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