Topic 1: Measurement and Uncertainties

Question 1

What is an order of magnitude?

Answer 1

A power of 10 (round to the nearest power of 10)

Question 2

What are the two extremes of size for distance?

Answer 2

Smallest is sub-nuclear particles (diameter of a proton) - 10^{-15} m
Largest is the visible universe - 10^{25} m.

Question 3

What are the two extremes of size for mass?

Answer 3

Smallest is an electron - 10^{-30} kg
Largest is the universe - 10^{50} kg

Question 4

What are the two extremes of time?

Answer 4

Smallest is the passage of light across a nucleus - 10^{-23} s
Largest is the age of the universe - 10^{18} s

Question 5

How do you compare orders of magnitude?

Answer 5

Divide larger number by smaller number (subtract exponents)

Question 6

Where can you find the metric multipliers?

Answer 6

In the IB data booklet under metric (SI) multipliers

Question 7

What are the 6 base or fundamental units you need to know?

Answer 7

Mass - kilogram (kg)
Length - metre (m)
Time - second (s)
Electric current - ampere (A)
Amount - mole (mol)
Temperature - Kelvin (K)

Question 8

What are derived units?

Answer 8

Units made from combinations of fundamental units (eg. newtons, joules, watts)

Question 9

What do you have to do to find derived units?

Answer 9

Substitute fundamental units into the formulas

Question 10

What are significant figures?

Answer 10

Digits that have value and are not placeholders

Question 11

What does a greater number of significant figures imply?

Answer 11

A greater degree of certainty

Question 12

What number of significant figures must the final answer be given to?

Answer 12

The least number of significant figures in the original data

Question 13

What are systematic errors?

Answer 13

When you get a measurement that is consistently bigger or smaller than the true value, due to faulty measurement practices

Question 14

What are some examples of systematic errors?

Answer 14

Incorrectly calibrated equipment
Equipment that does not read zero for a zero measurement
Parallax error
Making incorrect assumptions (eg. not taking into account friction)
Reaction time (to reduce this time a series of consecutive events then divide to find time for one)

Question 15

Are systematic errors reduced by making repeated measurements?

Answer 15

No

Question 16

What is some evidence for systematic errors?

Answer 16

The line of best fit for graph data doesn’t pass through the origin when it is expected to

Question 17

What are random errors?

Answer 17

When you are given a measurement that may be bigger or smaller than the true value (with equal probability)

Question 18

What are some examples of random errors?

Answer 18

The value you are measuring is constantly changing (eg. light intensity) - taking repeated measurements and averaging will give a more accurate reading by cancelling out errors in opposite directions

Question 19

What is some evidence for random errors?

Answer 19

Large error bars on graph

Question 20

Are random errors reduced by taking repeated measurements?

Answer 20

Yes

Question 21

Are mistakes uncertainties?

Answer 21

No

Question 22

What uncertainty do we use when using a stopwatch?

Answer 22

Generally +/- 0.1s

Question 23

What uncertainty do we use for measurements with a scale?

Answer 23

Generally +/- the smallest scale division

Question 24

What uncertainty do we use when a scale is used to measure a dimension that is difficult to judge?

Answer 24

One that is larger than +/- the smallest scale division

Question 25

What does some measuring equipment come with?

Answer 25

Its own stated uncertainty

Question 26

How can uncertainties be expressed?

Answer 26

In absolute, fractional, or percentage form

Question 27

What is absolute uncertainty form?

Answer 27

1.0 +/- 0.1 s
Uncertainty has 1sf
Measurement is given the same number of dp as the uncertainty
Unit is written after uncertainty

Question 28

What is fractional uncertainty form?

Answer 28

1.0 s +/- 1/10
Unit is written before uncertainty

Question 29

What is percentage uncertainty form?

Answer 29

1.0 s +/- 10 %
Uncertainty to 2sf
Unit written before uncertainty

Question 30

When we add or subtract measurements, what do we do with the uncertainties?

Answer 30

Always add them

Question 31

When we multiply/divide measurements, what do we do with the uncertainties?

Answer 31

Convert to % uncertainties, add % uncertainties, convert to an absolute value

Question 32

If you are multiplying or dividing by a number with no uncertainty, what do you do?

Answer 32

Divide both the uncertainty and measurement by the number

Question 33

If you are dealing with uncertainties and powers, what do we do?

Answer 33

Convert to % uncertainties, multiply % by the power, convert to an absolute value

Question 34

After a calculation, what should the final uncertainty be rounded to?

Answer 34

1sf, unless the leading figure is a 1, then we go to 2sf
Final measurement is given to same number of dp as uncertainty

Question 34

After a calculation, what should the final uncertainty be rounded to?

Answer 34

1sf, unless the leading figure is a 1, then we go to 2sf
Final measurement is given to same number of dp as uncertainty

Question 35

What is an accurate measurement?

Answer 35

One with small systematic error - ie. it is close to the true vale

Question 36

What is a precise measurement?

Answer 36

One that has small random error (repeated measurements will be close, but may not be correct)

Question 37

Are accurate measurements precise?

Answer 37

No - accurate doesn’t mean precise and precise doesn’t mean accurate

Question 38

How do you calculate the uncertainty of an average of a data set?

Answer 38

Use the half-range, remember to round to 1sf
Repeated measurements reduce the amount of random error in the data

Question 39

How do you graph uncertainties?

Answer 39

Using error bars

Question 40

How do you calculate uncertainty for gradient off a graph?

Answer 40

Draw the steepest line and least steep line you can reasonably draw within the error bars
The uncertainty is half the difference of these two

Question 41

How do you calculate uncertainty of y-intercept?

Answer 41

Find min and max y-int using min and max gradient lines - uncertainty in y-int is half the distance between these two

Question 42

How do you find the gradient of a line?

Answer 42

y=mx+c
Include uncertainties