1. IB Physics 12
Mr. Jean
September 18th, 2013

2. The plan:
Video clip of the day
Logging into Quest
Uncertainty

3. UNCERTAINTIES IN MEASUREMENTS
PROPERLY PROCESSING DATA

4. Texas University - Quest

13. Next Slide:
The next slide will tell you to wait until I accept you into the course.
I need to accept you into the course before you get enrolled into the course.

14. Once enrolled into the course:

15. Main Page:
Click on the IB physics 12 button to get to the student screen of the course.
Assignment #1 should appear under “Choose an assignment”.

16. Assignment #1:

17. About Assignments:
Quest assignments are similar, but not exact for each student.
So your answer may NOT be the same as your friends.
Assignments can be worked on with a partner, but each student is responsible for their own accounts assignment.

18. MEASUREMENTS WITH UNCERTAINTIES
Every measurement has a doubtful digit.
This ruler measures to the mm (0.1 cm)
Every measurement made with a ruler like this
has an uncertainty of ± 0.05cm.
This is half the smallest division.
This measurement is 1.02 ± 0.05 cm.
It lies somewhere between 0.97 cm and 1.07 cm.
Notice that the measurement and the uncertainty
have the same level of precision.

19. MEASUREMENTS WITH UNCERTAINTIES
Every measurement has a doubtful digit.
This stopwatch measures to 0.01 seconds.
This measurement could be 3min and seconds or
3 min and seconds.
This means the uncertainty is ±0.01 seconds and
the measurement is ± 0.01s.

20. Measurement, measurement
For IB labs, each measurement needs to be repeated at least 3 times.
For number of repeated values, we find the average.
The uncertainty in the average is plus or minus one-half of the range
between the maximum value and the minimum value.

21. Recording the data
Raw data should be presented in an easy to understand data table. The headings should state the name of the quantity, its symbol, the units it is measured in and its uncertainty.
Length
l/cm
Δl = ±0.1 cm
29.4
38.5
48.7
60.5

22. Recording the data
Of course, you will be measuring at least two variables. Here’s an example of using repeated values.
Length
l/cm
Δl =±0.1 cm
Time for 10 Periods
10T/s
Δ10T = ±0.01s
60.5
16.77
15.42
15.79

23. Recording the data
Of course, you will be measuring at least two variables. Here’s an example of using repeated values.
Length
l/cm
Δl =±0.1 cm
Time for 10 Periods
10T/s
Δ10T = ±0.01s
60.5
16.77
15.42
15.79
Average Time for 10 Periods
16.0

24. Recording the data
Of course, you will be measuring at least two variables. Here’s an example of using repeated values.
When dividing a measurement by a pure number, divide its uncertainty as well.
Length
l/cm
Δl =±0.1 cm
Time for 10 Periods
10T/s
Δ10T = ±0.01s
60.5
16.77
15.42
15.79
Average Time for 10 Periods
16.0
Average Period
1.60

25. Basic Rules
This is called the absolute or raw
uncertainty

26. Basic Rules

27. Basic Rules This is called the fractional or relative uncertainty
The relative uncertainty multiplied by 100% is called the percentage uncertainty.

28. Basic Rules

29. Basic Rules

30. Summary of the Basics
When adding or subtracting uncertainties, you ADD the ABSOLUTE uncertainties.
When multiplying or dividing uncertainties, you ADD the PERCENTAGE uncertainties.
When stating uncertainties the uncertainty must have 1 sig fig and must have the same level of precision of the measurement itself.

31. Reciprocal calculation
To straighten some curves, we use the reciprocal values. The uncertainties MUST be processed properly.

32. Power Function
Some graphs need a variable raised to an exponent to be linearized. Again, the uncertainties MUST be properly processed.

33. You Try
Calculate the volume of a sphere whose radius is measured to be

34. Gradient Uncertainties
Error bars must be shown on the graph for the variable with the most significant uncertainty.
Data point
Max value the data point could have
Min value the data point could have

35. Sample Graph
This data has the responding variable with a fixed absolute value of uncertainty of ±2 cm

36. Sample Graph
Here the uncertainty in the responding variable is a fixed percentage of 5%

37. Sample Graph
Here is the best straight line. The variables are proportional since the best straight line passes through the origin (accounting for error) and through each point.
But the slope measurement must have uncertainties associated with it as well.

38. Sample Graph
To get the uncertainty in the slope value, we will look at the maximum slope and the minimum slope then calculate half the range.

39. Sample Graph
The max slope is The min slope is The best slope is
We would record the slope as ±2.857.
With sig figs, it is 23 ±3.