# PH 2011 Milwaukee School of Engineering Uncertainties in Measurements Lab Report

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PH 2011

Milwaukee School of Engineering

PH

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Uncertainties in Measurements
Experiment Summary
This experiment was conducted to estimate the uncertainties in time measurement between two
bounces of a ping-pong ball. Random, systematic, and total uncertainties were determined. The
ping-pong ball was released to fall freely from a height of 1 m and bounce two times, during
which the time between the two bounces was obtained using a stopwatch.
Results
Table 1: Collected Data
Count

The time between 1st and
2nd bounce
[1/100 s]

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30

69
75
73
54
73
65
65
75
71
76
78
78
84
77
70
77
70
78
66
70
86
75
71
75
73
68
70
66
71
75

Average
Standard Deviation
Error on the mean

72
6
1

Table 2: Collected Data Grouped
The time between
1st and 2nd bounce
[1/100 s]
54
65
66
68
69
70
71
73
75
76
77
78
84
86

Number of times a
given measurement
was recorded
1
2
2
1
1
4
3
3
5
1
2
3
1
1

Number of Times Measured

Time Measured Between 1st and 2nd Bounce of
a Ping-pong ball
6
5

4
3

2
1
0
54

65

66

68

69

70

71

73

75

76

77

78

84

86

Time Between Bounces (1/100 s)

Figure 1: A Histogram Showing the Distribution of Times Between the 1st and 2nd Bounce of a
Ping-Pong Ball Dropped from a Height of 1 m.
The data collected during the 30 times was as shown in Table 1. The events yielding
same time were grouped to obtain Table 2 which was used to plot the histogram shown in Figure
1. The excel program was used to estimate the average time and standard deviation of the mean.
The average time, đť‘ˇĚ…, between the bounces was 0.72 s. The standard deviation of the mean, đť‘ đť‘ˇ ,
was 0.06 s. Analytically, 25 of the counts fell within one standard deviation of the mean, that is,

between 0.72-0.06 = 0.66 s and 0.72+0.66 = 0.78 s. This count meant that 5/6 of the data fell
within one standard deviation, a value that is greater than 2/3. From Figure 1, it is evident that
most of the data fall between 66 s and 78 s. The error on the mean which accounts for the
random error was estimated to be 0.01 s implying that the average value accounting for the error
was 0.72 Â± 0.01 s. The average value accounting for systematic error was 0.72 Â± 0.13 s.
Therefore, the average time taking into account the total uncertainty was 0.72 Â± 0.14 s.
Conclusion
The experiment confirmed the variation in measurements obtained from the same
experimental setup. These variations implied the presence of uncertainties in determining the
true measurement. Analysis of data collected from the same set up (one individual) yielded the
random error which was relatively smaller compared to the systematic error as it had been
theorized. The source of random error in the experiment count have been due to slight variations
in reaction time of the individual operating the stopwatch and slight variations on the surface
where the ping-pong ball w...

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