Topic 1: Measurement and Uncertainties Flashcards
What is an order of magnitude?
A power of 10 (round to the nearest power of 10)
What are the two extremes of size for distance?
Smallest is sub-nuclear particles (diameter of a proton) - 10^{-15} m
Largest is the visible universe - 10^{25} m.
What are the two extremes of size for mass?
Smallest is an electron - 10^{-30} kg
Largest is the universe - 10^{50} kg
What are the two extremes of time?
Smallest is the passage of light across a nucleus - 10^{-23} s
Largest is the age of the universe - 10^{18} s
How do you compare orders of magnitude?
Divide larger number by smaller number (subtract exponents)
Where can you find the metric multipliers?
In the IB data booklet under metric (SI) multipliers
What are the 6 base or fundamental units you need to know?
Mass - kilogram (kg)
Length - metre (m)
Time - second (s)
Electric current - ampere (A)
Amount - mole (mol)
Temperature - Kelvin (K)
What are derived units?
Units made from combinations of fundamental units (eg. newtons, joules, watts)
What do you have to do to find derived units?
Substitute fundamental units into the formulas
What are significant figures?
Digits that have value and are not placeholders
What does a greater number of significant figures imply?
A greater degree of certainty
What number of significant figures must the final answer be given to?
The least number of significant figures in the original data
What are systematic errors?
When you get a measurement that is consistently bigger or smaller than the true value, due to faulty measurement practices
What are some examples of systematic errors?
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)
Are systematic errors reduced by making repeated measurements?
No
What is some evidence for systematic errors?
The line of best fit for graph data doesn’t pass through the origin when it is expected to
What are random errors?
When you are given a measurement that may be bigger or smaller than the true value (with equal probability)
What are some examples of random errors?
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
What is some evidence for random errors?
Large error bars on graph
Are random errors reduced by taking repeated measurements?
Yes
Are mistakes uncertainties?
No
What uncertainty do we use when using a stopwatch?
Generally +/- 0.1s
What uncertainty do we use for measurements with a scale?
Generally +/- the smallest scale division
What uncertainty do we use when a scale is used to measure a dimension that is difficult to judge?
One that is larger than +/- the smallest scale division
What does some measuring equipment come with?
Its own stated uncertainty
How can uncertainties be expressed?
In absolute, fractional, or percentage form
What is absolute uncertainty form?
1.0 +/- 0.1 s
Uncertainty has 1sf
Measurement is given the same number of dp as the uncertainty
Unit is written after uncertainty
What is fractional uncertainty form?
1.0 s +/- 1/10
Unit is written before uncertainty
What is percentage uncertainty form?
1.0 s +/- 10 %
Uncertainty to 2sf
Unit written before uncertainty
When we add or subtract measurements, what do we do with the uncertainties?
Always add them
When we multiply/divide measurements, what do we do with the uncertainties?
Convert to % uncertainties, add % uncertainties, convert to an absolute value
If you are multiplying or dividing by a number with no uncertainty, what do you do?
Divide both the uncertainty and measurement by the number
If you are dealing with uncertainties and powers, what do we do?
Convert to % uncertainties, multiply % by the power, convert to an absolute value
After a calculation, what should the final uncertainty be rounded to?
1sf, unless the leading figure is a 1, then we go to 2sf
Final measurement is given to same number of dp as uncertainty
After a calculation, what should the final uncertainty be rounded to?
1sf, unless the leading figure is a 1, then we go to 2sf
Final measurement is given to same number of dp as uncertainty
What is an accurate measurement?
One with small systematic error - ie. it is close to the true vale
What is a precise measurement?
One that has small random error (repeated measurements will be close, but may not be correct)
Are accurate measurements precise?
No - accurate doesn’t mean precise and precise doesn’t mean accurate
How do you calculate the uncertainty of an average of a data set?
Use the half-range, remember to round to 1sf
Repeated measurements reduce the amount of random error in the data
How do you graph uncertainties?
Using error bars
How do you calculate uncertainty for gradient off a graph?
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
How do you calculate uncertainty of y-intercept?
Find min and max y-int using min and max gradient lines - uncertainty in y-int is half the distance between these two
How do you find the gradient of a line?
y=mx+c
Include uncertainties
