Physics 1 – Aug 26, 2016

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. 23.05 ± 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 = Ex: 0.01 / 23.05 = 0.000434 (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 100 Ex: 0.000434 * 100 = 0.0434 % (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 = 0.013 ± 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 = 0.013 ± 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 = 0.013 ± 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