1. STUDY GUIDE:
Page 11 -     Q7
Page 12 -     Q , 15
TEXT BOOK:
Page 3 and p4 -     Q1.1 ~1.5

2. Uncertainties and Errors

3. Errors
An experimental error just means there is a difference between the recorded value and the accepted/correct value. There are 2 main types of errors that occur throughout experimentation:
1) Random Errors
2) Systematic Errors

4. 1) Random Errors:
A random error normally occurs when reading values off a specific instrument. To reduce random errors, it is best to take a number of readings as the results tend to average out.
Examples:
1) The readability of the instrument
2) The observer being less than perfect
3) The effects of a change in the surroundings

5. 2) Systematic Errors:
A systematic error is normally due to the actual equipment used. As the same equipment is being used for each trial, repeating experiments will NOT reduce systematic errors.
Examples:
1) An instrument with zero error. To ensure accurate results, the value of the zero error should be subtracted from every reading.
2) An instrument being incorrectly calibrated
3) The observer being less than perfect in the same way for every measurement.

6. Precision and Accuracy
You will be required to understand the difference between a PRECISE and an ACCURATE result:
1) A precise experiment has a small random error.
2) An accurate experiment has a small systematic error.

7. Example:

8. Uncertainties
Any experimental value has some sort of uncertainty. We use uncertainties to give a possible range of values, instead of just stating one ‘perfect’ value.
There are 2 main methods of estimating uncertainty:
1) Estimating from first principles (used when taking measurements)
2) Estimating from several repeated measurements (used when you have a range of values)

9. 1) First Principles:
A different uncertainty range is used for analogue (rulers, measuring cylinders) and digital (electronic scales, stop watches) measuring devices:
1) Analogue = use half the smallest scale division
2) Digital = use the smallest scale division

10. Example:

11. 2) Repeated Measurements:
This is used when you have a number of values and their distance from the average is calculated.

12. Example:
The times for a ball to fall to the ground (in seconds) for 5 trials are:
2.01, 1.82, 1.97, 2.16 and 1.94
The average time was calculated to be 1.98s.
Therefore the largest and smallest possible reading are:
= 0.18s AND = 0.16s
The largest value is always taken as the uncertainty, therefore the uncertainty is written as: s

13. Representation of Uncertainties
Uncertainties can be written as either an absolute or percentage uncertainty.
1) Absolute = uncertainty is in same units as the final result
2) Percentage = uncertainty is written as a % of the final result

14. Example:
The mass of a block of wood is 10+1g and it’s volume is cm3.
* Please copy the example straight from your study guide; TOP box on page 8

15. Multiplication, Division and Powers
When 2 or more quantities are multiplied or divided and they both have uncertainties, the overall uncertainty is equal to the addition of the percentage uncertainties.
Power relationships are just a special case of this law.
* I will use the same example as the previous slide to demonstrate how to do this in class. Again please copy MIDDLE box on page 8 of study guide ready for my explanation next lesson

16. Addition and Subtraction
Whenever 2 or more quantities are added or subtracted and they both have uncertainties, the overall uncertainty is equal to the addition of the absolute uncertainty.
* Copy the example in the BOTTOM box on page 8 of your study guide. Again, I will explain in class next lesson.
- You do NOT have to copy “Other Functions” section