3. Propagation of Uncertainties

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3. Propagation of Uncertainties
Data analysis
3.6 More about Independent Uncertainties
Find the efficiency of electric motor lifting a
mass m through a height h.
The work accomplished is mgh.
The energy delivered to the motor is VIt.
h
Efficiency, e mgh/VIt
V voltage, I current, t time
m
2
3. Propagation of Uncertainties
Data analysis
3.6 More about Independent Uncertainties
Efficiency, e mgh/VIt
Fractional uncertainties for m, h, V and I 1
Fractional uncertainties for t 5
h
m
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3. Propagation of Uncertainties
Data analysis
3.6 More about Independent Uncertainties
Efficiency, e mgh/VIt
Fractional uncertainties for m, h, V and I 1
Fractional uncertainties for t 5
Fractional uncertainty of the efficiency
(old rule)
QC3-6
4
Data analysis
3. Propagation of Uncertainties
3.9 Example
A Measurement of g (gravitational acceleration)
from a simple pendulum experiment.
Pivot
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3. Propagation of Uncertainties
Data analysis
A Measurement of g (gravitational acceleration)
from a simple pendulum experiment.
3.9 Example
Product of 3 components
Pivot
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3. Propagation of Uncertainties
Data analysis
Measurement of g (gravitational acceleration)
from a simple pendulum experiment.
3.9 Example
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3. Propagation of Uncertainties
Data analysis
A Measurement of g (gravitational acceleration)
from a simple pendulum experiment.
3.9 Example
g 979 4 cm/s2
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3. Propagation of Uncertainties
Data analysis
3.9 Example
B Refractive index using Snells law
Snells law sini n sinr
i
Air
n Refractive index
Glass
r
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3. Propagation of Uncertainties
Data analysis
B Refractive index using Snells law
3.9 Example
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3. Propagation of Uncertainties
Data analysis
B Refractive index using Snells law
3.9 Example
Measured results
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3. Propagation of Uncertainties
Data analysis
B Refractive index using Snells law
3.9 Example
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3. Propagation of Uncertainties
Data analysis
3.9 Example
Microsoft Excel
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Data analysis
3. Propagation of Uncertainties
3.10 A More Complicated Example
Measurement of acceleration
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Data analysis
3. Propagation of Uncertainties
3.10 A More Complicated Example
Detector 1
Detector 2
q
Time trace
Detector 1
Detector 2
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Data analysis
3. Propagation of Uncertainties
3.10 A More Complicated Example
Measured results l 5.00 0.05 cm (1) s
100.0 0.2 cm (0.2) t1 0.054 0.001 s
(2) t2 0.031 0.001 s (3)
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Data analysis
3. Propagation of Uncertainties
3.10 A More Complicated Example
Velocity at Pos.1 v1 l/t1
Velocity at Pos.2 v2 l/t2
Measured results l 5.00 0.05 cm (1) s
100.0 0.2 cm (0.2) t1 0.054 0.001 s
(2) t2 0.031 0.001 s (3)
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Data analysis
3. Propagation of Uncertainties
3.10 A More Complicated Example
Measured results l 5.00 0.05 cm (1) s
100.0 0.2 cm (0.2) t1 0.054 0.001 s
(2) t2 0.031 0.001 s (3)
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Data analysis
3. Propagation of Uncertainties
3.10 A More Complicated Example
q1
q2
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Data analysis
3. Propagation of Uncertainties
3.10 A More Complicated Example
Measured results l 5.00 0.05 cm (1) s
100.0 0.2 cm (0.2) t1 0.054 0.001 s
(2) t2 0.031 0.001 s (3)
a 87.2 9 87 8 cm/s2