1. Lesson Objective
Review methods met to deal with uncertainties through example questions.
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2. Learning Objectives
To be able to calculate the absolute and percentage uncertainty of a measurement
To be able to combine these uncertainties to evaluate the overall uncertainty in a derived result
To be able to quote values including their uncertainties.
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3. Dealing with uncertainties: Calculations.
(Absolute) Uncertainties can be determined either by using ± ½ smallest scale division from a single measurement…
….or by using ± ½ range when you have a series of measurements.
% uncertainties can be calculated using:
(Absolute uncertainty/True value or average) x 100
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4. Dealing with uncertainties: Calculations.
Determining the radius of a thin metal wire: x Δx
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5. Dealing with uncertainties: Graphs.
When plotting graphs to obtain an unknown, the uncertainties can be found by …
Adding error bars to each point (top and bottom point may be sufficient but all should be done)
Draw a maximum and minimum LOBF
Find the values of gradients that correspond to this.
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6. Dealing with uncertainties: Graphs.
Calculate the 3 gradients, m, m1 and m2. In this example lets say we get the following answers: m = 17, m1 = 17.7 and m2 = 16.9
Calculate the total percentage uncertainty in m:
= 𝑚 1 − 𝑚 2 𝑚 ×100
= 17.7 − x 100
= 4.7%
= ± 2.35%
To quote your final value convert this into an absolute uncertainty:
17 x =
So our final answer becomes:
(17.0±0.4) ms -1
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7. Homework
Complete the task sheet applying the ideas about uncertainties. Deadline: 3.40pm ONE WEEK FROM TODAY. NB: This means it needs handing into my pigeon hole OR the trays but please ensure you put your name on it.
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