Penny Plummet
October 3, 2014
Introduction
The purpose of this lab was to design an experiment using a penny
and a stopwatch to determine the acceleration of gravity based on
the curve of best fit from the graphed data. The research question
was: “How does the height from which a 2005 penny is dropped
from a surface affect the time it takes for the penny to hit that
surface?” The hypothesis was that if the height from which a 2005
penny is dropped from a surface increases, then the time it takes for
the penny to hit that surface will increase, where t∝√ℎ.
Procedure and Materials
Sanjay measured 6 different heights on a wall and made a mark at
these heights using tape and a pencil. Sanjay held the 2.50 g, 2005
penny parallel to the floor with the bottom side of the penny at the
height of the mark on the piece of tape. He held the penny
approximately 1 cm away from the wall. The auditory cue, said by
Brian, was “1, 2, 3, drop.” Upon heading the word “drop,” Sanjay
released the penny and Brian started the timer. Brian looked only in
the area between the floor and approximately 10 cm up the wall.
Brian stopped the timer when he saw the penny hit the floor. Brian
recorded the data values for 10 trials at each height.
Diagram
viy
aT
h, t
yf
Constants and Equations
mp = 2.50 g
1
𝑦𝑓 = 𝑎𝑡 2 + 𝑣𝑖𝑦 𝑡 + 𝑦𝑖
2
viy = 0.00 m/s
h = yi
𝑡 𝑇 [ℎ] = √
yf = 0.00 m
−2ℎ
𝑎
aT = -9.8 m/s2
Data Summary
t10
tavg
STDEV
tavg2
|%RSD|
tT
|%err|
(s)
(s)
(s)
(s2)
of tavg
(s)
of t
0.32
0.36
0.05
0.13
12.66
0.45
21.29
0.57
0.46
0.11
0.21
23.22
0.55
16.32
0.49
0.54
0.04
0.29
7.34
0.60
9.81
0.64
0.58
0.09
0.33
14.87
0.64
9.84
0.68
0.84
0.65
0.69
0.09
0.09
0.42
0.48
Avg
14.41
12.66
14.50
0.68
0.71
Avg
4.52
3.26
12.36
Lab Partners: Sanjay Ganeshan
Graph
Penny Drop Time vs. Height
Average Drop Time, tavg (s)
Brian Manning, Section L
0.9
tavg[h]= 0.3521h0.7338
R² = 0.9955
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.8
1.3
1.8
2.3
Drop Height, h (m)
2.8
Analysis
The experiment produced a trend that is visible in the preceding
graph. The average |%RSD| is 14.50, indicating a low precision.
The average |%err| is 12.36, indicating a low accuracy. However,
the R2 value of .9955 indicates the strength of the math model. The
trend of data dropped from heights between 1.0 m and 2.5 m is
consistent with the hypothesis. Therefore, this trend would continue
if more tests were performed from different heights. At h=0 m, t
also equals 0 m. These are the limits for the experiment. The data
point that is farthest from the trend power function is for 1.5 meters,
and the data point that is closest to the trend power function is for
2.5 meters. The |%err| decreases with increasing height. The height
with the time that was closest to expected time, tT, was 2.5 m, which
had a |%err| of 3.26%. The tT was .71s, and the tavg was .69s. The
acceleration of gravity was found to be -11.51 m/s2 based on the
equation for the line of best fit. The EQ shown in the graph above
is a power equation that represents tavg vs h. The instantaneous slope
at a certain time t can be used to find the velocity at that time t.
Based on the power equation, the acceleration due to gravity (g) was
found to be -8.295 m/s2.
Conclusions
The data supported the hypothesis. From this experiment, it was
found that t is proportional to √ℎ. If the height from which a 2005
penny is dropped from a surface increases then the time it takes for
the penny to hit that surface will increase. √−2/𝑎 was found to
equal √ℎ. This was used to determine the acceleration of the penny,
-8.295 m/s2. However, it is known that gravity causes acceleration
on earth to equal -9.8 m/s2. Along with human error, a few other
possible sources of error may have affected the results. One possible
source of error is that Brian may have stopped the timer late since
he could only see from the floor to 10 cm up the wall. Furthermore,
the penny was dropped with horizontal distance of approximately 1
cm from the wall. Therefore, the penny may have rubbed against
the wall as it fell, resulting in friction and a lower magnitude
acceleration. The penny was also dropped parallel to the ground,
which may have resulted in increased air resistance and a decreased
calculated magnitude of acceleration due to gravity. The margin of
error (|%err|) is quite large, indicating the likelihood of multiple
sources of error. A future extension would be to conduct the
experiment at different altitudes and determine the effect of altitude
on the time is takes for a penny to travel a consistent distance when
in free fall. Also, an experiment could be conducted to determine
the effect that the orientation of the penny has on its acceleration
due to gravity.
Brian Manning
t1
(s)
0.35
0.31
0.51
0.55
0.50
0.64
t2
(s)
0.34
0.52
0.56
0.50
0.63
0.60
t3
(s)
0.34
0.36
0.60
0.53
0.78
0.71
t4
(s)
.34.
0.43
0.56
0.57
0.70
0.65
t5
(s)
0.31
0.31
0.47
0.50
0.64
0.63
t6
(s)
0.43
0.54
0.54
0.63
0.56
0.85
t7
(s)
0.32
0.60
0.56
0.45
0.65
0.66
t8
(s)
0.43
0.54
0.53
0.71
0.55
0.70
Section L
t9
(s)
0.36
0.45
0.57
0.68
0.78
0.63
t10
(s)
0.32
0.57
0.49
0.64
0.68
0.84
tavg
(s)
0.36
0.46
0.54
0.58
0.65
0.69
STDEV
(s)
0.05
0.11
0.04
0.09
0.09
0.09
tavg2 |%RSD|
(s2) of tavg
0.13
0.21
0.29
0.33
0.42
0.48
Avg
12.66
23.22
7.34
14.87
14.41
12.66
14.50
tT |%err|
(s)
of t
0.45 21.29
0.55 16.32
0.60 9.81
0.64 9.84
0.68 4.52
0.71 3.26
Avg 12.36
Linearized: Penny Drop Time2 vs. Height
Penny Drop Time vs. Height
0.6
0.9
tavg[h]= 0.3521h0.7338
R² = 0.9955
tavg2[h]= 0.1737h
R² = 0.911
0.5
Average Drop Time2, tavg2 (s2)
0.8
Average Drop Time, tavg (s)
IV1
IV2
IV3
IV4
IV5
IV6
h
(m)
1.000
1.500
1.750
2.000
2.250
2.500
October 3, 2014
Penny Plummet
0.7
0.6
0.5
0.4
0.4
0.3
0.2
0.1
0.3
0.0
0.2
0.8
1.3
1.8
Drop Height, h (m)
2.3
2.8
0.2
0.4
0.6
Drop Height, h (m)
0.8
1.0