Measurements and Uncertainties

Question 1

What are quantities?

Answer 1

Values which are numerical and measurable.

Question 2

What are the seven base/fundamental units and their quantities?

Answer 2

• Distance - metre m
• Time - seconds s
• Current - ampere amps
• Temperature - kelvin K
• Amount of substance - mole mol
• Mass - kilogram kg
  And also luminous intensity

Question 3

What are derived units?

Answer 3

These are units for physical quantities that are combinations of the fundamental units, eg. m s−1

Question 4

What does it mean to be homogenous?

Answer 4

The base units on both sides of the equation must be the same for it to be correct. Check this by evaluating derived units on both sides. Note: Homogenous equations may not be correct if the constants are wrong.

Question 5

What are orders of magnitude?

Answer 5

It is a rounded estimate for a value in the form of a power of 10, eg. 10^3, 10^-6 Used to compare magnitudes.

Question 6

What is uncertainty dependent upon?

Answer 6

• The resolution (smallest values on a scale) of the apparatus.
• The nature of the experiment and set up.

Question 7

How would you estimate uncertainty for the following measurements?

• Multiple measurements
• A single measurement
• A ruler or tape
• A digital measurement

Answer 7

• ± Half the range.
• ± Half of the resolution.
• ± The resolution (because of two uncertainties at either end)
• [find out]

Question 8

What are the three different forms which you can write uncertainty?

Answer 8

Absolute uncertainty eg. 10 ± 1
Fractional uncertainty eg. 10 ± 1/10
Percentage uncertainty dg. 10 ± 1/10 x 100 %

Question 9

How do you propagate uncertainties when adding or subtracting quantities?

Answer 9

Add the absolute uncertainties.

Question 10

How do you propagate uncertainties when multiplying or dividing quantities?

Answer 10

Add the percentage or fractional uncertainties.
y = a ± Δa where Δa is the absolute uncertainty.
If y = ab, Δy/y = Δa/a + Δb/b (fractional uncertainties)
For indicies, simply consider it as multiplication.
Note that constants can be ignored as they do not affect the percentage uncertainty.

Question 11

How do you graph uncertainties?

Answer 11

Use error bars in x and/or y directions.

Question 12

How do you treat lines of best fit with error bars?

Answer 12

Draw both a line of best fit, and a steepest and shallowest line going through the error bars. Find the gradient of the three lines. The uncertainty of m is (m(max) - m(min))/2

Question 13

How do you add vectors?

Answer 13

Join the ends together and find the resultant vector through trigonometry.

Question 14

How do you resolve vectors?

Answer 14

Split vectors that are at inconvenient angles into horizontal and vertical components (two new vectors). Eg. For vector V, create Vx and Vy.

Question 15

Explain the following terms used in experiments:

• Accuracy
• Precision
• Systematic error
• Random error

Answer 15

• The difference between the true value and a measurement - high accuracy has a small difference.
• The variation between repeated measurements - high precision has small variation.
• When there is a flaw in equipment or experiment design, so all data points deviate from the true value by a fixed amount.
• Fluctuations in measured data from limitations of the measuring device.

Question 16

What number of significant figures should you use for your answer and for the uncertainty?

Answer 16

• Answer: the smallest number of s.f.s in the data OR the number of d.p.s in the uncertainty
• Uncertainty: 1 s.f. always