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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:
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?
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