Measurements and uncertainties flashcards

Measurements and uncertainties underpins all experimental work in IB Physics. Students must distinguish between random and systematic errors, and understand that no measurement is exact. Every measured quantity carries an uncertainty, expressed as absolute, fractional or percentage uncertainty. When combining measurements, uncertainties must be propagated correctly: add absolute uncertainties for sums and differences, add percentage uncertainties for products and quotients, and multiply percentage uncertainty by the power for quantities raised to a power. Students should be able to assess precision and accuracy, draw error bars on graphs, and interpret the gradient and intercept of a best-fit line including its uncertainty. SI units and unit prefixes must be used consistently, and students should be able to estimate quantities to the correct order of magnitude. Understanding significant figures and how they relate to uncertainty is also essential throughout the course.

1. Card 1

   What is the difference between a random error and a systematic error?

   Random errors cause unpredictable scatter around the true value; systematic errors shift all readings consistently in one direction, affecting accuracy but not precision.

2. Card 2

   What does it mean to say a measurement is precise but not accurate?

   Precision means repeated readings are close together (small random error); accuracy means readings are close to the true value. Precise but inaccurate implies a systematic error is present.

3. Card 3

   How do you express the absolute uncertainty of a repeated measurement?

   Calculate the mean of the readings, then the absolute uncertainty is typically half the range of the readings (max minus min, divided by 2).

4. Card 4

   How do you convert an absolute uncertainty into a percentage uncertainty?

   Percentage uncertainty = (absolute uncertainty / measured value) x 100%. It allows comparison of uncertainties across different quantities regardless of units.

5. Card 5

   What rule applies when adding or subtracting two measured quantities?

   When adding or subtracting, you add the absolute uncertainties of each quantity to find the total absolute uncertainty of the result.

6. Card 6

   What rule applies when multiplying or dividing two measured quantities?

   When multiplying or dividing, you add the percentage uncertainties of each quantity to find the total percentage uncertainty of the result.

7. Card 7

   How do you find the uncertainty when a quantity is raised to a power n?

   Multiply the percentage uncertainty of the quantity by the magnitude of the power n. For example, if r has 2% uncertainty, r cubed has a 3 x 2% = 6% uncertainty.

8. Card 8

   What are error bars on a graph and what do they represent?

   Error bars are lines drawn through each data point extending in both directions to show the uncertainty in that measurement, either vertically, horizontally, or both.

9. Card 9

   How do you determine the uncertainty in the gradient of a best-fit line?

   Draw the steepest and shallowest lines of best fit still consistent with the error bars, then the uncertainty in the gradient is half the difference between these two extreme gradients.

10. Card 10

    What is the difference between the uncertainty of a single reading and an analogue instrument?

    For a digital instrument, uncertainty is plus or minus the last digit displayed; for an analogue instrument, it is typically plus or minus half the smallest scale division.

11. Card 11

    What is an order of magnitude estimate and why is it useful?

    An order of magnitude estimate gives the nearest power of ten for a quantity. It is useful for checking whether a calculated answer is physically reasonable without precise data.

12. Card 12

    What is the SI unit prefix for 10 to the power of minus 9, and give an example of its use?

    The prefix is nano (symbol n). An example is the nanometre (nm), used to measure wavelengths of visible light, which are roughly 400 to 700 nm.

• Students often add absolute uncertainties when they should add percentage uncertainties for multiplication and division, or vice versa, confusing the two propagation rules.
• Many students think that repeating a measurement and taking the mean eliminates systematic error, when in fact repetition only reduces the effect of random errors.
• A common error is recording a final answer to more significant figures than the data or its uncertainty justifies, implying a false level of precision in the result.

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