PHYS1006 Lecture Notes - Lecture 1: Decimal Mark, Significant Figures, Mount Everest
25 Jun 2018
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Lecture 1 Measurement
Uncertainty: The difference between the measured value and the true value. No instrument can
measure a quantity to a fine resolution. Eg. metre ruler us accurate to 1mm.
The uncertainty of an instrument is quoted as one half of the smallest division on the scale.
Eg. the smaller division on a metre ruler is 1mm, therefore uncertainty is 0.5mm. However,
when we take a measurement is taken at two places. Therefore, uncertainty UC is (0.5mm +
0.5mm = 1mm).
Treatment of Uncertainties
Rule 1. When measured quantities are added or subtracted, the final uncertainty is the sum of the
separate absolute uncertainty.
L L, W W
C = (L W) (L W)
C = (Length + Width) + (Uncertainty of Length +Uncertainty of Width)
Example 1
L = 21 0.1cm, W = 11 0.1cm
C = (21 + 11) (0.1 + 0.1)
C = 32 0.2
This means that the answer lies
somewhere between 32 – 0.2
and 32 + 0.2 31.8 and 32.2
Example 2
L = 21.3 0.1cm, W = 11.8 0.1cm
C = (21.3 + 11.8) (0.1 + 0.1)
C = 33.1 0.2cm
Perimeter = C * 2
Perimeter of the rectangle:
P = 2(33.1 0.2cm)
P = 66.2 0.4cm
Rule 2. When measured quantities are multiplied or divided, the fractional uncertainty is the sum of
the separate fractional uncertainties. If A is the measured quantity and the uncertainty in the
measured value of A is A then the fractional uncertainty is .
Fractional Uncertainty Formula:
Where A, B and C are measured quantities and n, m and p are the exponents (If one of the
measured quantities contains an index. Eg.T2)
Example 1
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Area = Length x Width
A = 21.3 x 11.8
A = 251.3cm2
Now we want to find the uncertainty:
Uncertainty is 0.1mm
A = (251 3)cm 2 (round the result to 3 significant figures because the original data given is 3 SF)
Example 2
An experiment to find the value of G (the acceleration due to gravity) saw a student measure the
length of a simple pendulum as 1.217 0.001m and its period as 2.25 0.04s. Calculate the value of
g and its associated uncertainty.
Formula:
Where: T = period
L = Length of Pendulum
G= Acceleration due to gravity – What we are trying to find
Square both sides
Multiply by G and divide by T
Substitute in known values (T and L)
Solve
G = 9.49m/s 2
Now we can calculate the uncertainty of G using the fractional uncertainty formula
Formula
Substitute in given pronumerals
Substitute in values
Multiply by G
Sub in G
Solve
Write the final answer
G = (9.49 0.35)m/s 2
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Document Summary
Uncertainty: the difference between the measured value and the true value. No instrument can measure a quantity to a fine resolution. The uncertainty of an instrument is quoted as one half of the smallest division on the scale. Eg. the smaller division on a metre ruler is 1mm, therefore uncertainty is 0. 5mm. However, when we take a measurement is taken at two places. When measured quantities are added or subtracted, the final uncertainty is the sum of the separate absolute uncertainty. C = (l w) ( l w) C = (length + width) + (uncertainty of length +uncertainty of width) L = 21 0. 1cm, w = 11 0. 1cm. C = (21 + 11) (0. 1 + 0. 1) This means that the answer lies somewhere between 32 0. 2 and 32 + 0. 2 31. 8 and 32. 2. L = 21. 3 0. 1cm, w = 11. 8 0. 1cm. C = (21. 3 + 11. 8) (0. 1 + 0. 1)
