Physics Lab Report Measurements
TITLE:
• Date:
• Experimentalist:
• Apparatuses:
1 Ruler and Samples
• Prepare a stick ruler which you can measure lengths in centimeters (cm). If you just have rulers with inches,
you can use it as well, but the centimeter stick is perferred. A ruler for thirty centimeter (about a foot) would
be fine.
• How long is the finest tick of the ruler?
[Unit: ]
• For this experiment, four samples of round shape are needed. Try to find four round things with perfect
circles in its crosssection, which are not too big, but different sizes. Something like coins, bottles, can, will
work.
• When the samples are perpared, put labels on samples, A, B, C, and D.
• Describe each sample briefly. Take a picture of samples with the ruler you have and attach it below.
Figure 1: Samples and Ruler
PHYS 2111 Experiment B. Measuring Lengths – Online 2
2 Sample A
2.1 Measuring the Diameter of Sample A:
• Measure diameters of the samples by using the device chosen six times. Make sure to follow the rule to get
the one more number guessed, after the finest tick. Write down measurements in Table 1.
Diameter Di Di − D¯ (Di − D¯)
2
[Unit: ] [Unit: ] [Unit: ]
1
2
3
4
5
6
Sum PDi Sum P(Di − D¯)
2
Average D¯ =
PDi
N
σD =
q
(Di−D¯)
2
N−1
Table 1: Measurement of the Diameters of the Sample, A.
• Add all measurements to get the sum, and obtain the average of your measurements of the longer length in
Table 1.
• Calculate the standard deviation for the statistical uncertaiinty of this measurement in Tabel 1. Write the
result below;
DA = D¯ ± σD = ± [Unit : ]
2.2 Circumference of Sample A
• By the rolling the sample over lines in Figure 2 and using a ruler, the circumference of sample A in Table 2.
Before you start rolling, put a mark on each sample to know where it starts. Understand the method very
well first and try to reduce uncertainty of this measurement.
Circumference Ci Ci − C¯ (Ci − C¯)
2
[Unit: ] [Unit: ] [Unit: ]
1
2
3
4
5
6
Sum PCi Sum P(Ci − C¯)
2
Average C¯ =
PCi
N
σC =
q
(Ci−C¯)
2
N−1
Table 2: Measurement of Circumference of Sample A
PHYS 2111 Experiment B. Measuring Lengths – Online 3
Circumference #1: C1 = mm
Circumference #2: C2 = mm
Circumference #3: C3 = mm
Circumference #4: C4 = mm
Circumference #5: C5 = mm
Circumference #6: C6 = mm
Figure 2: Measuring Circumferences of Sample A
PHYS 2111 Experiment B. Measuring Lengths – Online 4
• Calculate the average of the circumference in Table 2.
• Calculate the standard deviation of this measurement for the statistical uncertainty in Table 2.
Circumference Measured; CA = C¯ ± σC = ± [Unit : ]
3 Sample B
3.1 Measuring the Diameter of Sample B:
• By using the same method, measure the diameter of sample B in Table 3.
• Obtain the average and statistaical uncertainty of the measurement in the same table. Write the result below;
DB = D¯ ± σD = ± [Unit : ]
Diameter Di Di − D¯ (Di − D¯)
2
[Unit: ] [Unit: ] [Unit: ]
1
2
3
4
5
6
Sum PDi Sum P(Di − D¯)
2
Average D¯ =
PDi
N
σD =
q
(Di−D¯)
2
N−1
Table 3: Measurement of the Diameters of the Sample, B.
3.2 Circumference of Sample B
• By using the same method, measure the diameter of sample B in Figure 3, and write the the resulting
circumference measurements in Table 4.
• Obtain the average and statistical uncertainty of the circumference measurementsin Table 4.
Circumference Measured; CB = C¯ ± ∆C = ± [Unit : ]
4 Sample C
4.1 Measuring the Diameter of Sample C:
• By using the same method, measure the diameter of sample C in Table 5.
• Obtain the average and statistaical uncertainty of the measurement in the same table. Write the result below;
DC = D¯ ± σD = ± [Unit : ]
PHYS 2111 Experiment B. Measuring Lengths – Online 5
Circumference #1: C1 = mm
Circumference #2: C2 = mm
Circumference #3: C3 = mm
Circumference #4: C4 = mm
Circumference #5: C5 = mm
Circumference #6: C6 = mm
Figure 3: Measuring Circumferences of Sample B
PHYS 2111 Experiment B. Measuring Lengths – Online 6
Circumference Ci Ci − C¯ (Ci − C¯)
2
[Unit: ] [Unit: ] [Unit: ]
1
2
3
4
5
6
Sum PCi Sum P(Ci − C¯)
2
Average C¯ =
PCi
N
σC =
q
(Ci−C¯)
2
N−1
Table 4: Measurement of Circumference of Sample B
Diameter Di Di − D¯ (Di − D¯)
2
[Unit: ] [Unit: ] [Unit: ]
1
2
3
4
5
6
Sum PDi Sum P(Di − D¯)
2
Average D¯ =
PDi
N
σD =
q
(Di−D¯)
2
N−1
Table 5: Measurement of the Diameters of the Sample, C.
PHYS 2111 Experiment B. Measuring Lengths – Online 7
4.2 Circumference of Sample C
• By using the same method, measure the diameter of sample C in Figure 4, and write the the resulting
circumference measurements in Table 6.
Circumference #1: C1 = mm
Circumference #2: C2 = mm
Circumference #3: C3 = mm
Circumference #4: C4 = mm
Circumference #5: C5 = mm
Circumference #6: C6 = mm
Figure 4: Measuring Circumferences of Sample C
• Obtain the average and statistical uncertainty of the circumference measurementsin Table 6.
Circumference Measured; CC = C¯ ± ∆C = ± [Unit : ]
PHYS 2111 Experiment B. Measuring Lengths – Online 8
Circumference Ci Ci − C¯ (Ci − C¯)
2
[Unit: ] [Unit: ] [Unit: ]
1
2
3
4
5
6
Sum PCi Sum P(Ci − C¯)
2
Average C¯ =
PCi
N
σC =
q
(Ci−C¯)
2
N−1
Table 6: Measurement of Circumference of Sample C
5 Sample D
5.1 Measuring the Diameter of Sample D:
• By using the same method, measure the diameter of sample B in Table 7.
• Obtain the average and statistaical uncertainty of the measurement in the same table. Write the result below;
DD = D¯ ± σD = ± [Unit : ]
Diameter Di Di − D¯ (Di − D¯)
2
[Unit: ] [Unit: ] [Unit: ]
1
2
3
4
5
6
Sum PDi Sum P(Di − D¯)
2
Average D¯ =
PDi
N
σD =
q
(Di−D¯)
2
N−1
Table 7: Measurement of the Diameters of the Sample, D.
5.2 Circumference of Sample D
• By using the same method, measure the diameter of sample D in Figure 5, and write the the resulting
circumference measurements in Table 8.
• Obtain the average and statistical uncertainty of the circumference measurementsin Table 8.
Circumference Measured; CD = C¯ ± ∆C = ± [Unit : ]
PHYS 2111 Experiment B. Measuring Lengths – Online 9
Circumference #1: C1 = mm
Circumference #2: C2 = mm
Circumference #3: C3 = mm
Circumference #4: C4 = mm
Circumference #5: C5 = mm
Circumference #6: C6 = mm
Figure 5: Measuring Circumferences of Sample D
PHYS 2111 Experiment B. Measuring Lengths – Online 10
Circumference Ci Ci − C¯ (Ci − C¯)
2
[Unit: ] [Unit: ] [Unit: ]
1
2
3
4
5
6
Sum PCi Sum P(Ci − C¯)
2
Average C¯ =
PCi
N
σC =
q
(Ci−C¯)
2
N−1
Table 8: Measurement of Circumference of Sample D
6 Discussion
• Summarize the measurement of the diameter and circumference of four samples in Table 9.
Samples Diameter, D [Unit: ] Circumference, C [Unit: ]
A ± ±
B ± ±
C ± ±
D ± ±
Table 9: Summary of Measurements of the Shortest Length
• How are the precision (or statistical uncertainty) of circumference measurements are compared? Are they
close to each other? Which sample has the best precision? Which one the worst? Try to explain.
• What is a major source of the uncertainty? Discuss how you can reduce the uncertainty.
