IB A1.1 - Uncertainty

Get the Formative Assessment: FA01.1.docx

This assessment covers the following video flips:

  • 1A. Review Significant Figures

  • 1B. What uncertainty is

  • 1C. The propagation rule for adding and subtracting

  • 1D. The propagation rule for multiplying and dividing

  • 1E. The propagation rule for powers

The Formative Assessment solved:

Do these calculations – express the answer as a result and an uncertainty. For the multiplication and division, round the uncertainty to two places, and round the answer to match the decimal place of the uncertainty.

First Row:

(2.4 ± .1) + (4.5 ± .3) = ? (6.9 ± 0.4)

(7.2 ± .5) - (3.1 ± .4) = ? (4.1 ± 0.9)



Second Row:

(7.3 ± .2) x (9.5 ± .2) = ? (69.4 ± 3.4)

(12.7 ± .5) / (3.1 ± .2) = ? (4.10 ± 0.43)

Third Row:

(9 ± 5%) x (7 ± 8%) = ? (Give a percent uncertainty) (63 ± 13%)

(56 ± 2%) / (7 ± 3%) = ? (Give a percent uncertainty) (8 ± 5%)

Fourth Row:

(9.0 ± .2)2 (81.0 ± 3.6)

sqrt(25 ± 2) (5.00 ± 0.20?)


More Practice: (Get the uncertainty practice sheet: Worksheet-Uncertainty1.1.docx )

Any measurement or value in Physics will have an uncertainty. Here’s how to estimate that uncertainty:

· Measuring with a ruler: The uncertainty is ± half the smallest division on the ruler. If you measure something that is 12.4 cm long with a ruler that has mm divisions, then your uncertainty is ± .5 mm or ± .05 cm so you would say 12.4 ± .05 cm

· Using a digital readout: The uncertainty is ± the last digit. If you have an ammeter that reads 1.56 Amps, it would be 1.56 ± .01 Amps.

· Multiple trials of something with random error: You could say that it is the average, ± range/2. If you did 3 trials for the rocket lab, and a rocket stayed up in the air for 5.23, 5.25, 5.12, and 5.36 seconds, you could say that it is 5.24 (the average) ± .12 (the range/2, i.e. (5.36-5.12)/2).

Directions: The answers are on the side. (Uncertainties should be rounded to 1 or 2 sig figs, and the number of decimal places in the answer should not exceed the limit of the uncertainty)

Adding or subtracting – the uncertainty of a sum or difference is the sum of the uncertainties

2:37 HTPIB00C Uncertainty Sheet Addition and subtraction

Multiplying and/or dividing – if y = ab/c, then Dy/y = Da/a + Db/b + Dc/c (D reads uncertainty of) Round uncertainty to two sig figs.

3:46 Uncertainty Sheet multiplication and division part 2

(These are easy - % uncertainties are fractional uncertainties, so just add the %)

12%

9%

15%

0. What is the percent uncertainty of the area of a rectangle if the length is uncertain by 5%, and the width by 7%

1. What is the percent uncertainty of the volume of a cube if the sides each have a percent uncertainty of 3%?

2. A sphere has a radius with an uncertainty of 5%, what is the percent uncertainty of the volume?

2:45 The Uncertainty Sheet percent

Powers – if y = an, then Dy/y = |nDa/a| (D reads uncertainty of) Round uncertainty to two sig figs.

3:22 The Uncertainty Sheet Powers part 2

Word problems

0. A car goes 45 ± .5 m in 2.12 ± .11 seconds. What is the speed of the car, and what is the uncertainty of the speed?

1:50 The Uncertainty Sheet Word Problem 0

1. What is the area (with uncertainty) in square meters of a rectangular room that measures 3.5 x 4.2 m where both measurements have an uncertainty of .1 m?

1:55 The Uncertainty Sheet Word Problem 1

2. A staircase has 12 steps, each one being 11.7 ± .5 cm high. What is the total height of the staircase with uncertainty? (Add twelve together…)

1:21 The Uncertainty Sheet Word Problem 2

3. One board is 24.1 ± .5 cm long, and another is 25.3 ± .8 cm long. How much longer is the second than the first? Could the first possibly be longer?

0:44 The Uncertainty Sheet Word Problem 3

4. What is the area (with uncertainty) of a circle that is 12.0 cm ± .1 cm in radius?

1:55 The Uncertainty Sheet Word Problem 4

5. A sphere has a radius of 5.2 ± .2 cm. What is its volume in cubic centimeters?