Intro - 1 - Absolute and Relative Uncertainty

University:
High School
Course:
High School Physics
Academic year:

2024
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121

Pages:

11
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1 1

0.1 Absolute and Relative Uncertainty Measurement Uncertainty • The uncertainty of a reading is equal to half of the instrument’s smallest graduation • Recorded with a ± symbol in front of the uncertainty • Include digits that are certain & a final uncertain digit that is estimated • Ex. Ex. 0.1cm smallest 0.2mL smallest graduation graduation • The measurement uncertainty of an instrument is also called its absolute uncertainty. • Sometimes use ΔA or sometimes δA (delta) • Ex. Ex. 0.2mL smallest graduation 0.1cm smallest graduation - What happens when we combine measurements that each have uncertainty? - Does that thing change whether combination is addition or multiplication? Addition/Subtraction Rule of Uncertainties The absolute uncertainty of a sum or difference is equal to the sum of the absolute uncertainties involved. Ex: A rectangle has sides of 12.10 and 4.64 cm. It is measured with a ruler that has millimeter markings. What is the absolute uncertainty in perimeter? Question: How do we determine *how* important a measurement uncertainty is for a given measurement? • The ratio of the absolute uncertainty of a measurement to its best estimate is called the relative uncertainty. • Sometimes use (ΔA)/A or sometimes (δA)/A (Greek letter delta) • Ex. Ex. • Note: no units! Ratio, so units cancel. Multiplication/Division Rule of Uncertainties The relative uncertainty of a product or quotient is equal to the sum of the relative uncertainties involved. Note: I will always ask for the absolute uncertainties as final answers, so you can also use the following simplification: Multiplication example Ex: What is the absolute uncertainty in the area of an object that is 41.20 cm x 7.80 cm if measured with a millimeter ruler? Multiplication example Trigonometry Example (works for sin, cos or tan) • Ex: A protractor with degree markings measures an angle of ϴ = 30.0°. What is the absolute uncertainty in sin ϴ? • Degree marks gives Δϴ = 0.5° … therefore ϴ = (30.0 ± 0.5)° • sin 30.0° = 0.5 … but ϴ can be as low as 29.5° or high as 30.5° • Therefore sin ϴ can be as low as sin 29.5° = 0.4924 and as high as sin 30.5° = 0.5075. Find the larger positive difference! • sin 30.5° − sin 30.0° = 0.5075 − 0.5000 = 0.0075 = 0.008 • sin 30.0° − sin 29.5° = 0.5000 − 0.4924 = 0.0076 = 0.008 • Therefore 𝜟 𝐬𝐢𝐧 𝟑𝟎. 𝟎° = ±𝟎. 𝟎𝟎𝟖 11