AQA Physics A Level: Measurements and Errors

SI units

Fundamental (base) units of physical quantities.

SI unit of mass

Kg (kilogram).

Physical quantity measured in mol

Amount of substance.

SI unit of current

Amperes (A).

SI unit for temperature

K (kelvin) as this is the absolute scale.

SI unit of length

Metres (m).

Quantity measured in seconds

Time.

Are Newtons (N) an SI unit?

No, newtons are not fundamental, the SI units for force are kgms^-2.

SI units of energy

Kinetic energy = ½ x mass x velocity squared; Units = kg x (m/s) x (m/s) = kgm^2s^-2.

SI units of force

Force = mass x acceleration; Units = kg x ms^-2 = kgms^-2.

Express 60TΩ in standard form

6 x 10^13 (T is tera and the multiplier is 10^12).

Write 0.000003m with a suitable prefix

3µm.

Actual value of 8MΩ

8,000,000Ω or 8x10^6Ω.

6000pF in nF

6nF as 1 nano unit is 1000 pico units.

Multiplier associated with the prefix kilo (k)

1000 (10^3).

Multiplier associated with the prefix femto (f)

10^-15.

Express 7GΩ in standard form

7 x 10^9 Ω.

1 eV in J

1eV= 1.6 x 10^-19 J.

Express 6kWh in joules

6 kW = 6000 J/s; 1 hour= 3600s; 6kWh = 6000 x 3600 = 21.6 x 10^6 J = 21.6 MJ.

Convert 6.6pJ to eV

6.6pJ= 6.6 x 10^-12 J; Divide by 1.6 x 10^-19; 6.6pJ=4.1 x 10^7 eV (2sf) =41MeV.

Random error

An error that affects precision and cannot be completely removed, it causes differences in measurements.

Systematic error

An error that affects accuracy and occurs due to faults in equipment or experimental method, causing the result to be too large / small by the same amount each time.

Ways to reduce random error

●Take at least 3 repeats and calculate a mean. ●Use a computer or a data logger. ●Use higher resolution equipment.

Mass balance reading error

Systematic as the reading is too high by 4g each time.

Cause of parallax error

Reading a scale at a different angle each time; to correct this you should read scales at eye level to reduce parallax error.

How to reduce systematic error

Calibrate apparatus before using e.g. zero the balance when it is empty.

Electronic noise in ammeter

It is a random error as it will cause fluctuations in readings that affect precision and it cannot be removed.

Background radiation measurement

So that only the source's radioactivity is measured, by accounting for background radiation systematic error is reduced.

Precision

Precise measurements are consistent, they fluctuate slightly about a mean value - this doesn't indicate the value is accurate.

Repeatability

If the original experimenter can redo the experiment with the same equipment and method then get the same results it is repeatable.

Reproducibility

If the experiment is redone by a different person or with different techniques and equipment and the same results are found, it is repeatable.

Resolution

The smallest change in the quantity being measured that gives a recognisable change in reading.

Accuracy

If the value is close to the true value.

Absolute uncertainty

Uncertainty given as a fixed quantity e.g. 7 +/- 0.6 V.

Percentage uncertainty in 17 +/- 3 A

3/17 x 100 = 17.647 % = 18 % (2sf).

Fractional uncertainty of 8 +/- 0.5 m

0.5/8 = 1/16 (0.0625).

Reducing percentage and fractional uncertainty

Measure larger quantities e.g. a longer rope will have a smaller percentage uncertainty than a shorter one.

Time for 1 swing of pendulum

1 swing = 13/10 = 1.3s; Uncertainty = 0.3/10 = 0.03 s; Time = 1.3 +/- 0.03 s.

Difference between reading and measurement

Readings are when one value is found, measurements are when the difference between 2 readings is found.

Uncertainty of thermometer

The uncertainty in a reading is ± half the smallest division, so the uncertainty is ± 5/2 or ± 2.5 ℃.

Percentage uncertainty in 2cm line

Each end has uncertainty ±0.5mm, 0.5 + 0.5= 1 so uncertainty in the measurement = ±1mm; % uncertainty = 1/20 x 100 = 5% (2cm is 20mm); 2 ± 5% cm.

Uncertainty in charge of an electron

The uncertainty in a given value is ± the last significant digit: = 1.6 x 10^-19 ± 0.1 x 10^-19 C.

Mean and absolute uncertainty of drop times

The times for a ball to drop are measured as 3.2s, 3.6s, and 3.1s.

Mean time for a ball to drop

3.3 s

Absolute uncertainty of drop times

0.25 s

Correct format for uncertainty

7±0.7 V.

Uncertainty in thermometer measurement

0.5 K

Difference in temperature from 298±0.5 K to 273±0.5 K

25±1 K

Acceleration calculation from force and mass

a = 13 ± 6.2% m/s²

Percentage uncertainty in area of a circle

12% cm²

Line of best fit with error bars

Make sure the line of best fit goes through all the error bars.

Finding uncertainty in gradient of line of best fit

Calculate the gradient of the best and worst line, the uncertainty is the difference between the best and worst gradients.

Percentage uncertainty in gradient of line of best fit

Percentage uncertainty = | best gradient - worst gradient | / best gradient x 100

Uncertainty in y-intercept of line of best fit

| best y-intercept - worst y-intercept |

Percentage uncertainty in y-intercept

percentage uncertainty = | best y-intercept - worst y-intercept | / best y intercept x 100

Order of magnitude

Powers of ten which describe the size of an object.

Order of magnitude for the diameter of a nucleus

10^-15

Estimation in physics

A skill physicists must use to approximate values of physical quantities.

9.71 x 10^-21 to nearest order of magnitude

10^-20.

Mean of drop times

3.3 s

Uncertainty in temperature difference

1 K

Force applied to mass

91±3 N

Mass with uncertainty

7±0.2 kg

Area of a circle formula

Area = πr²

Percentage uncertainty in radius

6%