Uncertainties

 

Uncertainties

Estimate the uncertainty of your protractor.  1⁰ or 0.5⁰

Try and find your pulse. Then count how many beats per minute. Estimate the uncertainty. 1 bpm

How would you quote the following results from a repeated experiment?

2.00cm, 19.8cm, 1.99cm, 2.02cm, 197mm, 2.01cm  2.00+/-0.02cm

The length of a wooden block is found by placing it against a 30cm ruler (calibrated in mm). One end is judged to be nest to 62mm on the scale. The other end is nest to 1.5 cm on the scale. What is the length of the block? What is the uncertainty in the length? 4.7 cm If you take the uncertainty of your measure met to be 0.1cm then your total uncertainty is 0.2cm (1mm either end)

Three sets of students measure the value of g in the laboratory. Group 1 use a pendulum, group 2 use light gates, group 3 use a stopwatch and ruler and calculate the acceleration of a falling ball. Their results are below. All values in ms^-2

Group	1	2	3	4	5	mean g
1	9.79	9.87	9.76	9.79	9.78	9.798
2	9.67	9.66	9.66	9.68	9.67	9.668
3	7.48	8.97	10.32	11.61	10.67	9.81

 

Calculate the mean values. Plot all 3 groups’ results on a scatter graph.

Which is the most accurate?  Group 3 – nearest accepted value

Which is the most precise?          Group 2 – least scatter in results.

Which is the best experimental method? Group 1 good accuracy and precision

Group 3 has good accuracy but high scatter so random error - poor experiment probably due to method.

Group 2 has good precision but poor accuracy, probably due to systematic error – again poor experiment probably due to equipment

Give reasons for your answers.

A ring has an inner radius of , nd an outer radius of

.  

What is the width of the ring? Width = 8.0 -5.0 = 3.0 mm

Calculate the maximum and minimum width.

(8.0 + 0.2) – (5 – 0.2) = 3.4mm   (8.0 -0.2) – (5 + 0.2) = 2.6mm

So range of possible values is 2.6 -3.4 = 0.8mm.

Then state the uncertainty.

So width is  3.0+/- 0.4 mm (i.e. a spread of 8mm around the 3.0)

What is the uncertainty in the size of the hole? Holes don’t exist.

 

A set of students independently measure the period of a pendulum and obtain the following results

What would be quoted as the period and the uncertainty?   1.01+/-0.02s