1.2 Propagating Uncertainties

1.2 Propagating uncertainties

Remember…..if you are dividing or multiplying quantities you have to add the percentage uncertainties

If you are subtracting or adding quantities you have to add the absolute uncertainties

1. Natalia is 1.72 ± 0.01 m and Joon is 1.80 ± 0.01m. What is the difference in their heights?

2. Hanna and Alex are going to a party together. They travel a distance of 3000 ±100 m in a time of 400 ±10 seconds. What was their average speed?

3. Mr Porter is fitting a new carpet to his playroom. He measures the length of the room as 7.10 ±0.05 m and the width as 3.45 ±0.05 m. How much carpet should he buy to be “safe”?

4. Jan is trying to find the volume of a block of shortcake. He measures the length as 20.0 ±0.2cm, the width as 10.0 ±0.2cm and the height as 1.8 ±0.2cm. What is the volume of the shortbread?

5. Urszula throws a netball of mass 1.80 ±0.01kg with a speed of 8.2 ±0.2 m.s-1. What is the kinetic energy 2 of the netball? (Ek = ½mv )

The following text applies to questions 6-8: A student performs a simple experiment to find the average acceleration of a falling object. He drops a baseball from a building and uses a string and meter stick to measure the height the ball was dropped. He uses a stopwatch to find an average time of fall for 3 trials from the same height and reports the following data: h = 5.25 ± 0.15 m, t = 1.14 ± 0.06 s.

6. Use the equation a = 2h/t2 to determine the average acceleration and its uncertainty.

7. Comment on the accuracy of the acceleration result. Do you think the student made any mistakes? a) The uncertainty is high; probably a mistake in height measurement or reaction time with stopwatch. b) Although a < g, the result seems reasonably accurate since air resistance would reduce the ball's acceleration. c) The result does not agree with 9.8 m/s2, so the student must have made a mistake. d) The result can only be as accurate as the measurements; cannot tell if a mistake was made.

8. What one suggestion would you tell this student to improve the accuracy of the experimental result? a) Measure height better, maybe use a long tape measure that does not stretch. b) Improve the precision of the time with more trials or automatic device. c) Get an assistant to time when the ball hits the ground d) Reduce or eliminate air resistance.