1. Physics 1 – Aug 26, 2016 P3 Challenge – Do Now (on slips of paper)
Five students measured the diameter of a penny: 2.00 cm, 1.95 cm, 1.98 cm, 1.99 cm and 1.98 cm.
a) What is your best estimate of the diameter of a penny?
b) Estimate the uncertainty in this best estimate using the “1/2 of the range” method.
c) Write your best estimate with its uncertainty and unit.
Get out 1.1 Worksheet for p3-4 Homework check.
EXTRA CREDIT OPPORTUNITY:
Calculate the uncertainty using the standard deviation method by hand.

2. Objectives and Agenda IB 1.2 Uncertainties and Errors
Work with absolute, fractional and percentage uncertainties
Agenda for IB 1.2 Uncertainties and errors
Accuracy and Precision
Types of uncertainties
Error propagation, addition/subtraction
Error propagation, mult./div.
Error propagation, exponents and roots
Assignment: IB 1.2 Uncertainty and Errors Practice Sheet

3. Accuracy and Precision
Accuracy – low % error – how close is the Average to the Expected
Precision – small range – how close are the data to each other

4. Types of uncertainty reporting
Absolute uncertainty – a quantity giving the extremes a measured value falls within
Ex: Absolute uncertainty =∆x Ex ± 0.01 cm is a best estimate with its absolute uncertainty.
Will have the same unit as x.
Fractional uncertainty – the ratio of the absolute uncertainty to the mean value of a quantity. (Sometimes called the relative uncertainty.)
Ex: Fractional uncertainty = ∆𝒙 𝒙 Ex: / = (unitless)
Percent uncertainty – fractional uncertainty x 100%. (Not often used, but helps to build intuition about the meaning of a fractional uncertainty.)
Ex: Percent uncertainty = ∆𝒙 𝒙 x 100 Ex: * 100 = % (unitless)

5. Error propagation – Add/Subtract
When two quantities with uncertainty are added (or subtracted), their absolute uncertainties add.
Even if you subtract, the absolute uncertainties add.
Ex: Q = A + C
Find Q.
Add the uncertainties to find the uncertainty in Q.
Why does this rule work? (Consider Max and Min possible.)
IB formula summary of this rule: If: 𝑦 = 𝑎 ± 𝑏 then: 𝛥𝑦 = 𝛥𝑎+𝛥𝑏
For examples:
A =3.5 ± 0.5
B = ± 0.001
C = 1.25 ± 0.01
D = 7.1 ± 0.2

6. Error propagation – Mult/Div
For examples:
A =3.5 ± 0.5
B = ± 0.001
C = 1.25 ± 0.01
D = 7.1 ± 0.2
When two quantities with uncertainty are multiplied (or divided), their fractional uncertainties add.
Ex: Q = BD
Find Q.
Find the fractional uncertainties in B and D.
Add the fractional uncertainties to find the fractional uncertainty in Q.
Multiply Q’s fractional uncertainty by Q to find its ∆Q.
Why does this rule work? (Consider Max and Min possible.)
IB formula summary of this rule:

7. Error propagation – Powers and Roots
For examples:
A =3.5 ± 0.5
B = ± 0.001
C = 1.25 ± 0.01
D = 7.1 ± 0.2
When two quantities with uncertainty are raised to a power (or rooted), their fractional uncertainties, multiplied by their exponent, add.
Ex: Q = C3
Find Q.
Find the fractional uncertainties in C.
Multiply the fractional uncertainty by the exponent to find the fractional uncertainty in Q. (For Powers and Roots, sign does not matter.)
Multiply Q’s fractional uncertainty by Q to find its ∆Q.
Why does this rule work? (Consider Max and Min possible.)
IB formula summary of this rule:

8. Exit Slip - Assignment
For Error Propagation, identify the type of uncertainty you add for…
1) Adding and subtracting
2) Multiplying and Dividing
3) How do you handle Powers and Roots?
What’s Due on Tues Aug 30? (Pending assignments to complete.)
IB 1.2 Uncertainty and Errors Practice Sheet, P1-4
What’s Next? (How to prepare for the next day)
Read IB 1.2 p 16-20