Uncertainties
Aims
To be able to calculate the percentage
uncertainty of a measurement
To be able to combine these uncertainties to
evaluate the overall uncertainty in a derived
result
What are Uncertainties?
What do you think this
is?
It is very old!
It is GRB 090429B and is thought to be the remnants
of one of the first stars born after the Big Bang.
It is 13,140,000,000 ± 20,000,000 years old
Calculating Percentage Uncertainties
Reading on meter = 12.6 V
Finest division =
0.2 V
%Uncertainty = Finest Division x 100
Reading Taken
% Uncertainty = (0.2/12.6) x 100 = 1.6 %
Task
Calculate the percentage uncertainties for the
following measurements:
1.
3. 100m record of 9.6 s 1%
0.3%
4. Extension of 0.002m (2mm)
50%
5. Extension of 0.045m (45mm)
2%
2.
0.03%
Objectives
I can determine the uncertainty of a
measurement by looking at the scale, or by
using the value.
I can calculate the percentage uncertainty
of a measurement and comment about the
precision.
I can combine uncertainties to determine
the overall uncertainty in a derived result
where there are 2 variables.
I can combine uncertainties to determine
the overall uncertainty in a derived result
where there are 3 or more variables,
including powers.
I can make judgements about significant
sources of uncertainty and suggest
improvements to reduce their impact on the
final value.
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Combining Uncertainties
Suppose I want to work out the
density of the block…
Density =
Mass (kg)
Volume (m3)
Mass = 0.500 ± 0.001 kg
Volume = (6.25 ± 0.25) x 10-5 m3
To Work out the uncertainty in the density, I have to combine
the uncertainty in the mass with the uncertainty in the volume
How do we do it?
1. Work out the Percentage Uncertainty in
the volume and the mass.
2. Then add these together.
Work it out…
Answer…
4.2%
Objectives
I can determine the uncertainty of a
measurement by looking at the scale, or by
using the value.
I can calculate the percentage uncertainty of
a measurement and comment about the
precision.
I can combine uncertainties to determine
the overall uncertainty in a derived result
where there are 2 variables.
I can combine uncertainties to determine
the overall uncertainty in a derived result
where there are 3 or more variables,
including powers.
I can make judgements about significant
sources of uncertainty and suggest
improvements to reduce their impact on the
final value.
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THE RULES
What happens in the
formula
What to do to calculate
uncertainties
A x B or A ÷ B
Add percentage uncertainty
of A with percentage
uncertainty in B
A2
Double the percentage
uncertainty of A
An
Multiply the percentage
uncertainty by n
Uncertainty on a range of values
• Example:
The amount of time taken for a pendulum to swing back and forth is
recorded multiple times. The times recorded are...
• 1.42s, 1.37s, 1.40s, 1.42s, 1.40s, 1.39s, 1.37s
• The range of these measurements is: 1.42s - 1.37s = 0.05s
The absolute uncertainty is half of this: (0.05s)/2 = 0.025s = 0.03s (1sf)
The average of these measurements is 1.396s = 1.40s (rounding to 2dp,
the same as the uncertainty)
Our complete value with absolute uncertainty is:
• Time = 1.40 ± 0.03s
Objectives
I can determine the uncertainty of a
measurement by looking at the scale, or by
using the value.
I can calculate the percentage uncertainty of
a measurement and comment about the
precision.
I can combine uncertainties to determine
the overall uncertainty in a derived result
where there are 2 variables.
I can combine uncertainties to determine
the overall uncertainty in a derived result
where there are 3 or more variables,
including powers.
I can make judgements about significant
sources of uncertainty and suggest
improvements to reduce their impact on the
final value.
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Please complete worksheet on
uncertainty
• Submit to the Turnitin dropbox.