Practical skills: Errors and Uncertainties

Question 1

What are the SI base units for different quantities

Answer 1

Mass - kg
Length - m
Time - s
Current - A
Temperature - K
Amount of a substance - mol

Question 2

Derive the SI base units for force, voltage and pressure

Answer 2

Force:
F=ma
so F has units kgms^-2

Voltage:
V=E/Q
E=1/2mv^2
so E has units kgm^2s^-2
Q = It
so Q has units As
so V has units kgm^2s^-3A^-1

Pressure:
P=F/A
F has units kgms^-2
A has units m^2
so P has units kgm^-1s^-2

Question 3

Give the prefixes, symbols and their multiplier

Answer 3

Kilo (k) = 10^3
Mega (M) = 10^6
Giga (G) = 10^9
Tera (T) = 10^12
Centi (c) = 10^-2
Milli (m) = 10^-3
Micro (µ) = 10^-6
Nano (n) = 10^-9
Pico (p) = 10^-12
Femto (f) = 10^-15

Question 4

What affect does a random error have. Give an example of random error

Answer 4

They affect precision, meaning they cause unpredictable differences between measurements, causing a wider spread about the mean
e.g. environmental conditions

Question 5

What are the 3 ways you can reduce random error

Answer 5

Repeat measurements multiple times and calculate an average from them
Use computers/data loggers to reduce human error
Use equipment with a higher resolution

Question 6

What does systematic error affect. Give an example of systematic error

Answer 6

It affects accuracy, causing all measurements to be too high or too low compared to the true value, by the same amount each time. This is due to the apparatus or faults in the method.

examples:
- A balance that isn’t zeroed correctly (zero error)
- Reading the scale at the wrong angle (parallax error)

Question 7

What are 3 ways of reducing systematic error

Answer 7

1) Calibrate the apparatus by measuring a known value and seeing if it is right (e.g. weigh 1 kg on a mass balance)

2) In radiation experiments, measure background radiation first to exclude it from final results

3) Read the meniscus at eye level to reduce parallax error

Question 8

Define precision

Answer 8

Precision refers to how close the measurements are to each other, and therefore how much spread there is about a mean value. This does not mean the value is accurate

Question 9

Define accuracy

Answer 9

How close the measurement is to the true value

Question 10

Define a repeatable result

Answer 10

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

Question 11

Define a reproducible result

Answer 11

If an experiment can be redone by a different person or you redo it with different equipment/method, and the same result is found, the experiment is reproducible

Question 12

Define resolution

Answer 12

The smallest change in the quantity being measured that causes a different reading

e.g. ruler is 1mm

Question 13

Define uncertainty

Answer 13

The bounds in which the accurate value can be expected to lie

e.g. 20 degrees ± 2 degrees means the true value is somewhere between 18 and 22

Question 14

Describe the difference between absolute uncertainty, fractional uncertainty and percentage uncertainty

Answer 14

Absolute: given as a fixed value e.g. 7 ± 0.6V

Fractional: given as a fraction of the measurement
e.g. 7 ± 3/35 V

Percentage: given as a percentage of the measurement
e.g. 7 ± 8.6%

Question 15

Describe the difference between a reading and a measurement

Answer 15

A reading is where 1 value is found e.g. reading how high up the thermometer goes

A measurement is where you have to find the difference between 2 values e.g. in a ruler, you have to look at the start and end point

Question 16

How would you calculate the absolute uncertainty in a reading compared to a measurement

Answer 16

In a reading, the uncertainty is 1/2 of the smallest division (resolution)
e.g. the uncertainty on a thermometer reading is ± 0.5°C

In a measurement, there is uncertainty when you read both the start and end point, so it is double the uncertainty of a reading = the resolution
e.g. uncertainty of a ruler is ± 1mm

Question 17

How do you calculate the absolute uncertainty of a digital reading e.g. an ammeter

Answer 17

± the last significant digit

e.g. if the ammeter says 3.2 A, the uncertainty is ±0.1A

This means the resolution of the instrument affects the uncertainty

Question 18

How would you calculate the absolute uncertainty of repeated data

Answer 18

± range/2

You would write the answer as mean ± range/2

Question 19

How can you reduce uncertainty

Answer 19

Fix one end of a ruler so there is only uncertainty on one end

Reduce percentage uncertainty by measuring a larger quantity as the absolute uncertainty will be the same but the measurement will increase
e.g. if you want the time it takes for a pendulum to swing once, this could be 0.62 ± 0.1s but if you measure the time it takes for 10 swings, this is 6.2 ± 0.1s, which has 10x lower % uncertainty. you could then divide by 10 to get the time for 1 swing

Question 20

How many sf should you put uncertainty to

Answer 20

same as the data

Question 21

When you add or subtract 2 measurements, each with uncertainty, how do you calculate the uncertainty of the final measurement

Answer 21

Add the absolute uncertainties

Question 22

When you multiply/divide 2 measurements, each with uncertainty, how do you calculate the uncertainty of the final measurement

Answer 22

Add the percentage uncertainties

Also, this applies for raising values to a power because r^2 = r x r
Therefore you can do percentage uncertainty x the power to get the final %uncertainty

Question 23

How can you show uncertainty on a graph

Answer 23

Use error bars

• For each point, have a value for the mean, and then one for + the uncertainty and - the uncertainty

Question 24

How can you calculate the percentage uncertainty in the gradient of a graph

Answer 24

Measure the gradient of the line of best fit, (which passes through every error bar as close to the mean as possible)

Measure the gradient of the line of worst fit, which is either the steepest gradient possible, which still passes through every error bar or the shallowest gradient possible, which still passes through every error bar

Minus the gradients from each other (this is the absolute uncertainty)
and divide by the line of best fit gradient, then x100

You can also work out the % uncertainty between the 2 lines of worst fit

Question 25

How do you calculate the percentage uncertainty in the y-intercept

Answer 25

Find the y intercept for the line of best and worst fit

Minus them from each other (this is the absolute uncertainty) and then divide by the y intercept of the line of best fit

You can also work out the % uncertainty between the 2 lines of worst fit

Question 26

How can you give your answer to the nearest order of magnitude

Answer 26

give it to the nearest power of 10

e.g. 8.8x10^-21 to the nearest order of magnitude is 10^-20

(5 orders of magnitude larger is 10^5 times larger so 10^7 is 10^5 times bigger than 10^2)

Question 27

What are 7 common estimations used in physics to remember

Answer 27

diameter of an atom = 10^-10 m

Wavelength of UV light ≈ 10^-9 m

Distance between the earth and the sun ≈ 1.5 x 10^11 m

Mass of a hydrogen atom ≈ 10^-27 kg

Mass of a car ≈ 1000 kg

Power of a light bulb ≈ 60W

Atmospheric pressure ≈ 10^5 Pa