Percentage uncertainty and Absolute uncertainty (EXCLUSIVE)

Question 1

Or rather, what are all the uncertainties?

Answer 1

1. Uncertainty (resolution)
2. Uncertainty (repeats)
3. % Uncertainty
4. % Uncertainty using equation
5. Absolute uncertainty

Question 2

Explain Uncertainty (resolution)

Answer 2

How far off your measurement may be due to the precision of the equipment
e.g. if a time of 2.11 sec is measure the uncertainty is the smallest measurement you can take so 0.01 sec
Time = 2.11± 0.01s

Question 3

Explain Uncertainty (repeats)

Answer 3

How far off your mean measurement may be due to the range in your repeats
e.g. if a time of 2.11 sec, 2.31sec, 2.21sec is measured in 3 repeats then the mean = 2.21s
The uncertainty is the range /2
= (2.31 - 2.11)/2 = 0.1

Time = 2.21 ± 0.1s

Question 4

Explain % Uncertainty

Answer 4

The uncertainty as a % of the value
So for time = 2.11 ± 0.01,
% uncertainty = 0.01/2.11 x 100 = 0.47%

• Keep values to same decimal places as equipment as a rule of thumb
• The larger the measurement the smaller the & uncertainty will be

Question 5

Explain % Uncertainty using an equation

Answer 5

If a question asks for the % uncertainty in speed but your not measuring speed directly, you will need to use an equation to help you

Speed = distance/time
(Ya needa use uncertainties in distance and time to work out uncertainties in speed)

Let’s say distance was 0.1m and the smallest division is 0.001m and the speed was 0.31s and the smallest division is 0.01s, then the uncertainties of each are:

Distance % uncertainty = 0.000/0.1 x 100 = 1.00%
Time % uncertainty = 0.01/0.31 x 100 = 3.23%

The total % uncertainty is always the other uncertainties added together so the % uncertainty of speed would be:
Speed % uncertainty = 1.00 + 3.23 = 4.23%

• If you need to work out area and square a distance, then add the uncertainty twice
• If you need to work out volume cube a distance, then add the uncertainty three times

Question 6

Explain Absolute uncertainty

Answer 6

This is putting the % uncertainty back into an actual value, so if we use the speed example again and we have worked out a value of 5.96m/s but we know that % uncertainty is 4.23%, we have to work out 4.32% of 5.96 so:

Absolute uncertainty in speed = 4.32/100 x 5.96 = 0.26m/s

So we can say our experimental value for speed is:
5.96 ± 0.26m/s