1. Physics and Physical Measurement
Orders of Magnitude

2. What is Physics Physics tries to explain the universe.
From the very big - to the very small
To do this the range in magnitudes will be huge

3. Why is this important?
Sometimes we only need an approximate value for a quantity – World Population?
You might want to make a rough estimate to check a calculation.
Rough Estimate: round off all numbers to one significant figure.
Can only be accurate to a factor of 10

4. SI Prefixes

5. Comparisons between orders of Magnitude
Diameter of an atom 10-10m does not sound that much larger than the diameter of a proton in its nucleus m
The ratio between them is 105 bigger, bigger.
Same ratio between the size of a railway station and the earth.

6. Ranges Distance: 10-15m sub nuclear particle 1025m visible universe
Mass:
10-30kg electron
1050kg Universe
Time:
10-23s light across nucleus
1018s age of universe

7. Examples
Estimate the volume of a circular lake 1km across and with an average depth of 10m
Estimate the thickness of a page of your textbook

8. Examples
1. List assumptions you would have to make to estimate the number of Mechanics in Mombasa
2. How many hours you have spent in school so far in your life
3. How many marbles are in a one litre jar?

9. SI Units Any measurement must have two components - the number
- the unit
In order for units to be understood they need to be defined.
In science we use the International System of units (SI).

10. Fundamental units Quantity Unit Symbol Mass kilogram kg Length metre m
Time
second s
Electric current
ampere A
Amount of substance
mole
mol
Temperature
kelvin K
Luminous Intensity
candela cd

11. Metric (SI) Multipliers

12. Derived Units
All other measurements can be expressed as different combinations of derived fundamental units
E.g speed = distance
time
Unit of speed = metres
second
= m s
= ms-1

13. Derived Units Quantity Symbol Unit name Unit Symbol Area A
Square metre m2
Volume V
Cubic metre m3
Velocity v
Metres per second
ms-1
Acceleration a
Metres per second squared
ms-2
Density p
Kilogram per cubic metre
kg m-3

14. Problems Express the following quantities in fundamental units: 12 km
12 GA
17.3 µm
12.6 mA

15. Derived units with special names
Some more complicated or commonly used units have been given special names.
Quantity name
Quantity Symbol
Unit Name
Symbol
Formula
Frequency f
Hertz Hz
1/ t
s-1
Force F
Newton N
F=ma
Kg ms-2

16. More Conversions Change to fundamental Units 1. 748 cm2
mm2
mm3
Mm2
Km3

17. Easy conversions
15h
20 OC
60kWh
7.43 eV

18. How can we reduce errors
Take 5 minutes to come up with a few ways to improve the accuracy and precision of an experiment

19. Uncertainties Random Systemic Misreading apparatus
Errors in calculations
Errors copying raw data to lab report
Systemic
Poor Calibration
Consistent bad reaction time
Parallax error

20. Experimental Technique
Accuracy: this is an indication of how close measurement is to its accepted value.
An accurate experiment would have low systemic error.
Systemic errors can be reduced by recalibrating equipment
Random errors can be reduced by repeating readings and averaging.

21. Sig Figs
Number of sig figs should reflect the precision of the input data to a calculation.
For multiplication and division, the number of sig figs in result should not exceed that of the least precise value upon which it depends.

22. Example The following data was obtained, Density = mass ÷ volume
Length = 20.5 cm
Height = 8.4 cm
Thickness = 10.2 cm
Mass = g
Density = mass ÷ volume
Calculate density of brick and give answer to appropriate sig figs

23. Absolute Uncertainties Analogue vs Digital
Analogue: uncertainty of half the limit of reading,
- metre stick, 5m + 0.5m
Digital: uncertainty one whole limit of the reading
- Wrist watch s + 1s
- Digital stopwatch 0.1 s + 0.1s

24. Fractional Uncertainties
Fractional uncertainty = absolute uncertainty
measurement
Example: Metre rule measures the length of an object to 22m,
What is fractional uncertainty?

25. Percentage Uncertainty
Percentage uncertainty = fractional X 100
From previous example
Percentage uncertainty = X 100 = 1.79%
Measurement can be shown three ways
- Length = 28mm + 0.5mm (absolute)
- Length = 28mm (fractional)
- Length = 28mm % (percentage)

26. Adding Subtracting uncertainties
Turn to page 5 of data book:
For addition and subtraction, absolute uncertainties can be added
If y = a + b
Then ∆y = ∆a + ∆b

27. Multiplication, division and powers
Turn to page 5 of data book:
For multiplication, division and powers, percentage uncertainties can be added
If y =ab c
Then ∆y = ∆a + ∆b + ∆c
y a b c

28. Examples
Using the following data, calculate the density of the object and associated percentage and absolute uncertainties due to uncertainty in measuring apparatus
Mass, m = 1.37 kg kg density = mass
Width, w = m m volume
Length, l = m m
Height, h = 0.116m m

29. Practice Errors
Use metre stick to calculate the following areas/volumes and express uncertainties in calculation.
(hint – if calculation requires multiplication use percentage uncertainties)
area of square in corridor
Volume of wall cupboard
Area of desk.

30. Representing uncertainties on a graph
Instead of plotting points on a graph we sometimes plot lines representing the uncertainty in the measurements.
These lines are called error (uncertainty) bars and if we plot both vertical and horizontal bars we have what might be called "error rectangles“.

31. Graph with error bars y (m) + 0.3m Vertical component shows + 0.3m
Horizontal component
shows s
x (s) s

32. Practice Plot a graph of this data, (Spring Constant)
Add uncertainty bars
Draw line of best fit
Calculate the gradient of best fit line
Find y intercept
Force F/N
∆F = + 0.5N
Extension x / mm
∆x = + 0.5mm 1 4 2 7 3 13 16 5 20 6 23 29 8 32

33. Maximum and minimum slopes
A point may lie anywhere inside the error rectangle and still be valid.
Draw two other (dashed) best fit lines showing maximum and minimum values of slope and y intercept
Calculate maximum gradient
Calculate minimum gradient

34. Uncertainty in the intercept
Using value from best fit, together with maximum and minimum values we can express
Spring constant = 0.25Nmm Nmm-1