PHYS 253 - Module 1 - Lab 3
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Embry-Riddle Aeronautical University *
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253
Subject
Aerospace Engineering
Date
Apr 3, 2024
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docx
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Measurements and Uncertainty
PRE-LAB QUESTIONS
1.
Use Figure 4 to measure the diameter of the quarter.
Main scale reading: 24
mm
Vernier scale reading: 1
∗
0.05
=
0.05
mm
Main scale + Vernier scale: 24.05
mm
2.
Why is uncertainty important to consider when reporting data?
Measurement uncertainty is important because it provides an understanding of the limitations and potential errors associated with any measurement.
©eScience Labs, 2014
Figure 4: A quarter being measured by a caliper.
Measurements and Uncertainty
EXPERIMENT 1: RULERS VS. CALIPERS
Data Sheet
Table 1. Ruler and Caliper Measurements
Object
Ruler
Caliper
Measurement
(cm)
Uncertainty
(cm)
Measurement
(cm)
Uncertainty
(cm)
Marble Diameter
1 cm
1.5 ±
0.1 cm
2 cm
2 ±
0.5 cm
Washer (Outer
Diameter)
1.73 cm
1.73 ±
0.1 cm
1.62 cm
1.62 ±
0.1 cm
Washer (Inner
Diameter)
0.9 cm
0.9 ±
0.5 cm
0.53 cm
0.53 ±
0.1 cm
Washer Thickness
0.5 cm
0.5 ±
0.5 cm
0.03 cm
0.03 ±
0.1 cm
String Length
612 cm
612 ±
0.1 cm
599 cm
599 ±
0.1 cm
Styrofoam® Cup
Height
8.12 cm
8.12 ±
0.1 cm
8 cm
8 ±
0.1 cm
Post-Lab Questions
1.
Compare the measurements for objects using the ruler and caliper and write a general
statement on when it is more beneficial to use a ruler rather than a caliper.
Choosing between a ruler and a caliper depends on the specific requirements of the
measurement task. Rulers are preferable for quick and simple measurements of larger
objects, while calipers are better suited for tasks demanding a higher degree of accuracy,
especially for smaller and more intricate dimensions. Selecting the appropriate tool depends
on the precision needed for the particular application.
2.
Comment on accuracy vs. precision for rulers and calipers.
Rulers:
Rulers generally offer accuracy for larger measurements but may lack precision due
to larger scale increments. They are suitable when a close approximation is sufficient.
Calipers:
Calipers excel in precision, providing accurate measurements for smaller details. Their fine scale increments make them ideal for tasks requiring a high level of accuracy.
Rulers prioritize accuracy over precision, making them suitable for general measurements, ©eScience Labs, 2014
Measurements and Uncertainty
while calipers prioritize precision, ensuring accurate readings for more intricate dimensions.
3.
What are the sources of uncertainty when using a ruler and caliper?
Sources of Uncertainty for Rulers:
Parallax Error:
Misalignment of the eye with the measurement markings on the ruler can
introduce errors, especially when viewing from an angle.
Instrumental Limitations:
Rulers may have inherent imperfections, such as uneven
markings or slight deformities, affecting measurement accuracy.
Human Error:
Inconsistent or imprecise placement of the ruler on the object or
misinterpretation of the markings can contribute to uncertainties.
Temperature Effects:
Changes in temperature may cause the ruler to expand or contract,
leading to variations in measurements.
Sources of Uncertainty for Calipers:
Zero Error:
Calipers may have a zero point that is not perfectly aligned, resulting in
systematic errors if not properly calibrated.
Instrumental Precision:
While calipers are designed for precision, variations in
manufacturing quality can affect their accuracy.
Friction:
Friction in the moving parts of the caliper can lead to inconsistent readings,
especially if not properly lubricated.
Operator Skill:
The accuracy of caliper measurements depends on the skill and experience
of the person using them.
Temperature Effects:
Like rulers, calipers can be sensitive to temperature changes,
causing expansion or contraction and influencing measurements.
©eScience Labs, 2014
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Measurements and Uncertainty
EXPERIMENT 2: THE SPRING FORCE SCALE
Data Sheet
Table 2. Spring Scale Measurements
Object
5 N Spring
Scale Weight (g)
Uncertainty (g)
10 N Spring
Scale Weight (g)
Uncertainty (g)
Masking
Tape
71 g
71
±
10 g
82 g
71
±
10 g
Stopwatch
32 g
32
±
10 g
43 g
43
±
0
g
Set of
Masses
82 g
82
±
5 g
91 g
91
±
5 g
Modeling
Clay
490 g
490 ±
10 g
498 g
498
±
5 g
Post-Lab Questions
1.
What are the advantages and disadvantages of using a spring scale to measure weight?
Advantages of Using a Spring Scale to Measure Weight:
Ease of Use:
Spring scales are user-friendly and straightforward, making them easy for individuals of various skill levels to operate.
Portability:
Spring scales are often compact and lightweight, making them easily portable for measuring weight in different locations.
Cost-Effective:
Compared to some other types of scales, spring scales tend to be more affordable, making them accessible for a wide range of applications.
Quick Measurements:
Spring scales provide rapid measurements, making them suitable for tasks where speed is essential.
Durability:
Spring scales are generally robust and durable, with fewer delicate components that may be prone to damage.
Disadvantages of Using a Spring Scale to Measure Weight:
Limited Precision:
Spring scales may lack the precision required for highly accurate measurements, especially in scientific or industrial settings.
Non-Linearity:
The relationship between the force applied and the scale's indication may not be perfectly linear, leading to potential errors, particularly at extreme ends of the scale.
Limited Weight Range:
Spring scales are typically designed for specific weight ranges, and
using them outside these ranges may result in inaccurate measurements.
Temperature Sensitivity:
Changes in temperature can affect the accuracy of spring scales,
as the elasticity of the spring may vary.
©eScience Labs, 2014
Measurements and Uncertainty
Subject to Wear:
Over time, the spring in a spring scale may lose its elasticity, leading to a decline in accuracy. Regular calibration is necessary to maintain precision.
2.
What are sources of uncertainty when using a spring scale? Calibration Issues:
The accuracy of a spring scale relies on proper calibration. If the scale
is not regularly calibrated, it may lead to measurement errors.
Non-Linearity:
The relationship between the applied force and the scale reading may not
be perfectly linear. Non-linear behavior can introduce uncertainties, especially at the
extremes of the scale.
Hysteresis:
Hysteresis occurs when the spring in the scale does not return to its original
position after a load is applied and then removed. This can result in discrepancies in
subsequent measurements.
Temperature Effects:
Changes in temperature can affect the elasticity of the spring,
leading to variations in the readings. Spring scales may not provide accurate measurements
if used in environments with fluctuating temperatures.
Parallax Error:
Incorrect reading due to viewing the scale from an angle can introduce
parallax errors. Ensuring that the scale is viewed straight-on helps minimize this source of
uncertainty.
Sensitivity to External Forces:
External forces, such as air currents or vibrations, can
influence the measurements on a spring scale, introducing uncertainties.
Wear and Tear:
Over time, the spring in a spring scale may experience wear and lose its
elasticity. This can result in a decline in the scale's accuracy, emphasizing the importance of
regular maintenance.
Operator Technique:
Inconsistent application of force or improper use of the scale by the
operator can lead to uncertainties in measurements.
Limited Resolution:
Spring scales may have limited resolution, making it challenging to
discern small changes in weight accurately.
©eScience Labs, 2014
Measurements and Uncertainty
EXPERIMENT 3: THE STOPWATCH
Data Sheet
Table 3. Time Data for Dropped Marble
Drop (Trial)
Time (s)
1
0.67 s
2
0.70 s
3
0.81 s
4
0.51 s
5
0.60 s
Post-Lab Questions
1.
What are the advantages and disadvantages of using a stopwatch to measure time?
Advantages of Using a Stopwatch to Measure Time:
Precision:
Stopwatches provide high precision for measuring time intervals, making them
suitable for tasks that require accurate timing, such as sports events or scientific
experiments.
Ease of Use:
Stopwatches are user-friendly and straightforward, with simple controls for
starting, stopping, and resetting the timer.
Portability:
Stopwatches are typically compact and portable, allowing for easy
transportation and use in various settings.
Versatility:
Stopwatches can be used for a wide range of activities, from sports and fitness
training to scientific experiments and cooking.
Real-Time Monitoring:
Stopwatches allow for real-time monitoring of elapsed time,
enabling users to track the duration of an event or activity precisely.
Disadvantages of Using a Stopwatch to Measure Time:
Limited Resolution:
Stopwatches may have limited resolution, making it challenging to
measure very small time intervals accurately.
Human Reaction Time:
The accuracy of timing events with a stopwatch can be influenced
by the reaction time of the person operating it, especially when manual button pressing is
involved.
Subject to Human Error:
Human error, such as starting or stopping the stopwatch at the
wrong moment, can introduce inaccuracies in timing measurements.
Battery Dependence:
Stopwatch operation relies on batteries, and if they run out or the
device malfunctions, it can impact the reliability of timing measurements.
©eScience Labs, 2014
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Measurements and Uncertainty
Not Suitable for Continuous Monitoring:
Stopwatches are designed for discrete time
measurements and may not be ideal for continuous monitoring over extended periods.
Limited Features:
Basic stopwatches may lack advanced features like lap timing or data
storage, limiting their functionality in certain applications.
2.
What are sources of uncertainty when using a stopwatch?
Human Reaction Time
: The time it takes for the operator to initiate or stop the stopwatch
can introduce uncertainties, especially in situations requiring precise timing.
Parallax Error:
Viewing the display of the stopwatch from an angle can lead to parallax
errors, affecting the accuracy of the recorded time.
Button Response Time:
The responsiveness of the stopwatch buttons may vary, and
delays in pressing or releasing the buttons can contribute to timing inaccuracies.
Limited Resolution:
Stopwatches may have limited resolution, making it challenging to
measure very small time intervals accurately.
Battery Status:
If the stopwatch relies on batteries, uncertainties can arise if the battery
level is low or if the batteries fail during the timing process.
External Conditions:
Environmental factors such as temperature, humidity, or altitude can
influence the performance of the stopwatch, leading to variations in timing accuracy.
Mechanical Wear:
Mechanical stopwatches may experience wear and tear over time,
affecting their precision. Regular maintenance is essential to minimize this source of
uncertainty.
Inconsistent Starting and Stopping:
Inconsistent operation of the stopwatch, such as
pressing the buttons unevenly or at different angles, can introduce uncertainties in timing
measurements.
Limited Features:
Basic stopwatches may lack features like lap timing or data storage,
limiting their functionality and introducing uncertainties in specific applications.
Operator Skill:
The skill and experience of the person operating the stopwatch can
influence the accuracy of timing measurements.
©eScience Labs, 2014
Measurements and Uncertainty
EXPERIMENT 4: DENSITY OF THE MASS SET
Data Sheet
Table 4. Mass Set Density Data
Quantity
Measurement Uncertainty Height (cm)
2.10 cm
±
0.025
Radius (Diameter/2), r (cm)
Or
Base Edge Length, b (cm)
2.80 cm
±
0.025
Volume, V (cm
3
)
134 c m
3
N/A
Mass (g)
100 g
Density (g/cm
3
)
9.75 g
cm
3
N/A
©eScience Labs, 2014
Measurements and Uncertainty
Table 5: Known Densities of Various Materials
Material
Density at 20ºC
Aluminum
2.70 g/cm
3
Copper
8.92 g/cm
3
Lead
11.34 g/cm
3
Nickel
8.90 g/cm
3
Silver
10.50 g/cm
3
Steel
7.80 g/cm
3
Zinc
7.14 g/cm
3
Post-Lab Questions
1.
Use Table 5 to determine what material the mass set is made of. Be sure to take your
uncertainty into consideration. It is made of zinc.
©eScience Labs, 2014
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