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.

5:46 Uncertainty Sheet multiplication and division part 1

3:46 Uncertainty Sheet multiplication and division part 2

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

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.

3:48 The Uncertainty Sheet Powers part 1

3:22 The Uncertainty Sheet Powers part 2

Word problems

21.2 ± 1.3 m/s

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

14.7 ± .8 m2

.77?

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

140.4 ± 6.0 cm

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

1.2 ± 1.3 cm

Yes

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

452.4 ± 7.5 cm2

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

589 ± 68 cc

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

2:10The Uncertainty Sheet Word Problem 5