Penny Drop Lab
September 13, 2016
Jack Mao, Section A
Graph
The purpose of the lab is to design a good scientific
experiment using independent and dependent variables, vary
and debug data collections methods to achieve the best
measurement precision, and organize, analyze, and present data
and findings in an effective way. How does increasing height,
measured from the floor to the closest face of a flat penny, affect
the time the penny takes to hit the floor after the penny is
dropped? The higher the penny is, the longer it takes for the
penny to be dropped, where t α √h.
Procedure and Materials
Time vs. Height
0.9
0.8
Average Drop Time, tavg (s)
Introduction
Lab Partners: R. Senthilkumar, M. Farraher
0.7
t = 0.3887h0.548
R² = 0.9642
0.6
0.5
0.4
0.3
0.2
0.1
For this experiment, a penny from 1995 was placed on a
piece of paper. Jack lifted the paper with the penny at five evenly
spaced heights, starting from 40 cm above ground to 200 cm
above ground. Melissa recorded the time it took for the penny to
drop to the ground using a stopwatch. Melissa counted “one, two,
three, go” before starting the stopwatch. As soon as Jack heard
the word ‘go’, he pulled the paper under the penny. As soon as
Melissa heard the penny drop to the ground, she stopped the
stopwatch. Rithika wrote the time on a piece of paper. This
procedure was repeated ten times for all heights.
Diagram
viy
a
Constants and Equations
m = 2.52 g
viy = 0 m/s
yi = h
yf = 0 m
at = - 9.80 m/s2
h, t
1
𝑦𝑖 = 𝑎𝑡 2 + 𝑣𝑖𝑦 𝑡 + 𝑦𝑖
2
−2ℎ
𝑡𝑇 [ℎ] = √
𝑎𝑇
0.0
0.000
0.500
1.000
1.500
2.000
2.500
Drop Height, h (m)
Analysis
The correlation in the experimental data suggests that the
higher the drop height, the more time it takes for the penny to
drop to the ground.
The minimum value of the curve of best fit approximates the
time it takes for the penny to drop 40 cm to the ground. The
maximum value, likewise, suggests the time it takes for the penny
to drop 80cm to the ground. The slope of the graph decreases,
suggesting a possibility that at a certain point, the change in
height would be negligible. Because the graph is a polynomial
function with positive exponent, there is no limit as the drop
height increases.
The absolute value of average percent RSD is greater than 10
percent, suggesting low precise. The absolute value of the
percent error is also greater than 10 percent, suggesting low
accuracy. The mathematical model, however, is strong because
the R2 value is greater than 0.95.
The acceleration caused by gravity can be determined by
using a point from the line of best fit and substituting the values
to the equation 𝑡𝑇 [ℎ] = √
−2ℎ
𝑎𝑇
. By using the value h = 1.2 m and
using it in the equation for line curve of best fit, one can find that
t = 0.430. Substituting t and h into 𝑡𝑇 [ℎ] = √
Data Summary
h
tavg
STDEV
%RSD
tT
|%err|
(m)
(s)
(s)
of tavg
(s)
of t
0.400
0.25
0.03
14.04
0.29
4.25
0.800
0.32
0.02
6.92
0.40
20.80
1.200
0.41
0.08
19.20
0.49
16.54
1.600
0.55
0.04
7.38
0.57
3.22
2.000
0.56
0.04
6.86
0.64
13.13
Avg
10.88
Avg
13.59
−2ℎ
𝑎𝑇
shows that the
gravitational acceleration is -12.98 m/s2.
Conclusions
The data supports the hypothesis. The experiment
determined that the time it took for the pennies to drop
increased at a non-linear rate. The sources of error could come
from factors such as air resistance. Air resistance could slow the
rate at which the penny falls. The position of the penny on the
paper under the penny could also affect the time it takes for the
penny to drop. Future extensions of the lab could include how the
orientation of the penny affect the time it takes for the penny to
drop to the ground.