MEASUREMENTS AND THEIR ERRORS

Question 1

SI UNIT MASS

Answer 1

kg

Question 2

SI UNIT LENGTH

Answer 2

m

Question 3

SI UNIT TIME

Answer 3

s

Question 4

SI UNIT TEMPERATURE

Answer 4

K

Question 5

SI UNIT AMOUNT OF SUBSTANCE

Answer 5

mol

Question 6

SI UNIT ELECTRICAL CURRENT

Answer 6

A

Question 7

Tera T

Answer 7

10^12

Question 8

Giga G

Answer 8

10^9

Question 9

Mega M

Answer 9

10^6

Question 10

Kilo k

Answer 10

10^3

Question 11

Centi c

Answer 11

10^-2

Question 12

Milli m

Answer 12

10^-3

Question 13

Micro µ

Answer 13

10^-6

Question 14

Nano n

Answer 14

10^-9

Question 15

Pico p

Answer 15

10^-12

Question 16

Femto f

Answer 16

10^-15

Question 17

1eV in J

Answer 17

1.6x10^-19J

Question 18

Precision

Answer 18

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

Question 19

Repeatability

Answer 19

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

Question 20

Reproducability

Answer 20

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

Question 21

Resolution

Answer 21

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

Question 22

Accuracy

Answer 22

A measurement close to the true value is accurate.

Question 23

Random Errors

Answer 23

Random errors affect PRECISION, meaning they cause differences in measurements which causes a spread about the mean. You cannot get rid of all random errors.
An example of random error is electronic noise in the circuit of an electrical instrument.

Question 24

Reducing Random Errors

Answer 24

Take at least 3 repeats and calculate a mean, this method also allows anomalies to be identified.

Use computers/data loggers/cameras to reduce human error and enable smaller intervals.

Use appropriate equipment, e.g a micrometer has higher resolution (0.1 mm) than a ruler (1 mm).

Question 25

Systematic Errors

Answer 25

Systematic errors affect ACCURACY and occur due to the apparatus or faults in the experimental method. Systematic errors cause all results to be too high or too low by the same amount each time.
An example is a balance that isn’t zeroed correctly (zero error) or reading a scale at a different
angle (this is a parallax error).

Question 26

Reducing Random Errors

Answer 26

● Calibrate apparatus by measuring a known value (e.g. weigh 1 kg on a mass balance), if the reading is inaccurate then the systematic error is easily identified.
● In radiation experiments correct for background radiation by measuring it beforehand and excluding it from final results.
● Read the meniscus (the central curve on the surface of a liquid) at eye level (to reduce parallax error) and use controls in experiments.

Question 27

Parallax Error

Answer 27

A systematic error, reading a scale at a different
angle. Read the meniscus (the central curve on the surface of a liquid) at eye level.

Question 28

Zero Error

Answer 28

A systematic error, a balance that isn’t zeroed correctly.

Question 29

Uncertainty

Answer 29

The uncertainty of a measurement is the bounds in which the accurate value can be expected to lie e.g. 20°C ± 2°C , the true value could be within 18-22°C

Question 30

Absolute Uncertainty

Answer 30

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

Question 31

Fractional Uncertainty

Answer 31

uncertainty as a fraction of the measurement e.g. 7 V +/- 3/35

Question 32

Percentage Uncertainty

Answer 32

uncertainty as a percentage of the measurement e.g. 7 +/- 8.6%V

Question 33

Reducing percentage and fractional uncertainty

Answer 33

you can measure larger quantities

Question 34

Readings

Answer 34

Readings are when one value is found e.g. reading a thermometer

Question 35

Measurements

Answer 35

measurements are when the difference between 2 readings is found, e.g. a ruler (as both the starting point and end point are judged).

Question 36

Uncertainty in a Reading

Answer 36

The uncertainty in a reading is ± half the smallest division,
e.g. for a thermometer the smallest division is 1°C so the uncertainty is ±0.5°C

Question 37

Uncertainty in a Measurement

Answer 37

The uncertainty in a measurement is at least ±1 smallest division: e.g. a ruler, must include both the uncertainty for the start and end value, as each end has ±0.5mm, they are added so the uncertainty in the measurement is ±1mm.

Question 38

Uncertainty in Digital Readings

Answer 38

Digital readings and given values will either have the uncertainty quoted or assumed to be ± the
last significant digit e.g. 3.2 ± 0.1 V, the resolution of an instrument affects its uncertainty.

Question 39

Uncertainty in Repeated Data

Answer 39

For repeated data the uncertainty is half the range (largest - smallest value), show as: mean ± (range/2)

Question 40

Reducing Uncertainty

Answer 40

By fixing one end of a ruler as only the uncertainty in one reading is included.

By measuring multiple instances:
e.g. to find the time for 1 swing of a pendulum by measuring the time for 10 giving e.g. 6.2 ± 0.1 s, time for 1 swing is 0.62 ± 0.01s (the uncertainty is also divided by 10).

Question 41

Sig.fig in uncertainties

Answer 41

Uncertainties should be given to the same number of significant figures as the data.

Question 42

UNCERTAINTIES: Adding/Subtracting data

Answer 42

ADD ABSOLUTE UNCERTAINTIES
A thermometer with an uncertainty of 0.5 K shows the temperature of water falling from 298-0.5 K to 273-0.5K, what is the difference in temperature?
298-273 = 25K 0.5 + 0.5 = 1K (add absolute uncertainties) difference = 25 1 K

Question 42

UNCERTAINTIES: Multiplying / dividing data

Answer 42

ADD PERCENTAGE UNCERTAINTIES
E.g. a force of 91 3 N is applied to a mass of 7 +/- 0.2 kg, what is the acceleration of the mass?
F=ma A=f/m
91/7=13ms^-2 (3/91x100)+(0.2/7x100)=6.2%
13x0.062=0.8
13+/-0.8ms^-2

Question 43

UNCERTAINTIES: Raising to a power

Answer 43

MULTIPLY PERCENTAGE UNCERTAINTY BY POWER
The radius of a circle is 5 +/- 0.3 cm, what is the percentage uncertainty in the area of the circle?
Area = π x 25 = 78.5 cm2
Area = πr
%uncertain in radius=0.3/5x100=6%
%in area (r^2)= 6*2=12%
78.5+/-12%cm^2

Question 44

Percentage Uncertainty

Answer 44

(uncertainty/value)x100

Question 45

Uncertainties on Graphs

Answer 45

Uncertainties are shown as error bars on graphs,
e.g. if the uncertainty is 5mm then have 5 squares of error bar on either side of the point. A line of best fit on a graph should go through all error bars (excluding anomalous points).

Question 46

Uncertainty in a Gradient

Answer 46

The uncertainty in a gradient can be found by lines of best and worst fit, this is especially useful when the gradient represents a value such as the acceleration due to gravity:
● Draw a steepest and shallowest line of worst fit, it must go through all the error bars.
● Calculate the gradient of the line of best and worst fit, the uncertainty is the difference between the best and worst gradients.

Question 47

Percentage Uncertainties on Graphs Equation

Answer 47

(best gradient-worst gradient)/best gradient x 100
(best y intercept - worst y interecpt)/best y intercept x100

Question 48

Orders of Magnitude

Answer 48

Orders of magnitude - Powers of ten which describe the size of an object, and which can also be
used to compare the sizes of objects.
E.g: The diameter of nuclei have an order of magnitude of around 10^−14
100 m is two orders of magnitude greater than 1m.

Question 49

How is Estmation Used

Answer 49

Estimation is a skill physicists must use in order to approximate the values of physical quantities, in order to make comparisons, or to check if a value they’ve calculated is reasonable.