Uncertainties

Aims To be able to calculate the percentage uncertainty of a measurement To be able to combine these uncertainties to evaluate the overall uncertainty in a derived result

A Speed camera takes two images of a moving car and works out speed by calculating distance/time. How do you think this image would help somebody appeal their fine in court?

E D C B A Objectives Start of Lesson End of Lesson Red Amber Green I can determine the uncertainty of a measurement by looking at the scale, or by using the value.   I can calculate the percentage uncertainty of a measurement and comment about the precision. I can combine uncertainties to determine the overall uncertainty in a derived result where there are 2 variables. I can combine uncertainties to determine the overall uncertainty in a derived result where there are 3 or more variables, including powers. I can make judgements about significant sources of uncertainty and suggest improvements to reduce their impact on the final value. E D C B A

What are Uncertainties? What do you think this is? It is very old! It is GRB 090429B and is thought to be the remnants of one of the first stars born after the Big Bang. It is 13,140,000,000 ± 20,000,000 years old

Calculating Percentage Uncertainties Reading on meter = 12.6 V Finest division = 0.2 V %Uncertainty = Finest Division x 100 Reading Taken % Uncertainty = (0.2/12.6) x 100 = 1.6 %

Task Calculate the percentage uncertainties for the following measurements: 1. 3. 100m record of 9.6 s 1% 0.3% 4. Extension of 0.002m (2mm) 50% 5. Extension of 0.045m (45mm) 2. 2% 0.03%

E D C B A Objectives Start of Lesson End of Lesson Red Amber Green I can determine the uncertainty of a measurement by looking at the scale, or by using the value.   I can calculate the percentage uncertainty of a measurement and comment about the precision. I can combine uncertainties to determine the overall uncertainty in a derived result where there are 2 variables. I can combine uncertainties to determine the overall uncertainty in a derived result where there are 3 or more variables, including powers. I can make judgements about significant sources of uncertainty and suggest improvements to reduce their impact on the final value. E D C B A

Combining Uncertainties Suppose I want to work out the density of the block… Mass (kg) Density = Volume (m3) Mass = 0.500 ± 0.001 kg Volume = (6.25 ± 0.25) x 10-5 m3 To Work out the uncertainty in the density, I have to combine the uncertainty in the mass with the uncertainty in the volume

How do we do it? Work out the Percentage Uncertainty in the volume and the mass. 2. Then add these together.

Work it out… Answer… 4.2%

E D C B A Objectives Start of Lesson End of Lesson Red Amber Green I can determine the uncertainty of a measurement by looking at the scale, or by using the value.   I can calculate the percentage uncertainty of a measurement and comment about the precision. I can combine uncertainties to determine the overall uncertainty in a derived result where there are 2 variables. I can combine uncertainties to determine the overall uncertainty in a derived result where there are 3 or more variables, including powers. I can make judgements about significant sources of uncertainty and suggest improvements to reduce their impact on the final value. E D C B A

THE RULES A x B or A ÷ B A2 An What happens in the formula What to do to calculate uncertainties A x B or A ÷ B Add percentage uncertainty of A with percentage uncertainty in B A2 Double the percentage uncertainty of A An Multiply the percentage uncertainty by n

INSTRUCTIONAL SLIDE Beach Ball Questioning Write about 15 labels to stick on the ball. These should be simple formulae with letters, e.g. AB A/B, X2 , πr2h etc. Stick on labels. Throw ball to a student, student picks label that is nearest left thumb and say how they would calculate the uncertainty. Then throw ball back to you

Independent Learning Task There is a colour coded question grid on your worksheet. You need to choose 3 questions in a line (can be horizontal, vertical, diagonal, doesn’t have to be through the middle box). Beware however… Blue (easy) to Yellow (taxing) to pink (challenging). Blue questions gain 1 mark, yellow gain 2 and pink gain 3 marks. Make sure you clearly label your answers You have 12 minutes

Assessment Swap your work with your partner and assess each others work using the mark scheme. PINK – 3 MARKS YELLOW – 2 MARKS BLUE – 1 MARK Write down your partners mark on the white board and display when asked.

Self Assessment What did you do well? What mistakes did you make How could you improve?

E D C B A Objectives Start of Lesson End of Lesson Red Amber Green I can determine the uncertainty of a measurement by looking at the scale, or by using the value.   I can calculate the percentage uncertainty of a measurement and comment about the precision. I can combine uncertainties to determine the overall uncertainty in a derived result where there are 2 variables. I can combine uncertainties to determine the overall uncertainty in a derived result where there are 3 or more variables, including powers. I can make judgements about significant sources of uncertainty and suggest improvements to reduce their impact on the final value. E D C B A

Discussion In your recent experiment about determining the Young Modulus… What were the most significant sources of uncertainty? How did you arrive at this decision? Explain how you would you improve the precision of the final value (lower the combined uncertainty)

E D C B A Objectives Start of Lesson End of Lesson Red Amber Green I can determine the uncertainty of a measurement by looking at the scale, or by using the value.   I can calculate the percentage uncertainty of a measurement and comment about the precision. I can combine uncertainties to determine the overall uncertainty in a derived result where there are 2 variables. I can combine uncertainties to determine the overall uncertainty in a derived result where there are 3 or more variables, including powers. I can make judgements about significant sources of uncertainty and suggest improvements to reduce their impact on the final value. E D C B A