The Realm of Physics, Measurement and
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Transcript The Realm of Physics, Measurement and
THE REALM OF PHYSICS,
MEASUREMENT AND
UNCERTAINTY
Topics 1.1 and 1.2 on IB Syllabus
1.1 The Realm of the Universe
Question 1: What range of sizes
does the universe hold?
Powers of 10 Video
http://www.youtube.com/watch?v=A2cmlhfdxuY&fea
ture=fvst
A power of 10 (102, 105 , 10-12) are called orders
of magnitudes. What do they represent?
Some notes…
Question 2: How do we measure and
express measurement in physics?
1.
2.
Fundamental Units
Derived Units
1. Fundamental Units
Derived Units
Unit Prefixes:
See your IB Physics data booklet pg. 2
Some notes
1012 Microphones = 1 megaphone
500 millinaries = 1 seminary
2000 mockingbirds = 2 kilomockingbirds
10 cards = 1 decacards
10-6 fish = 1 microfiche
1021 picolos = 109 los = 1 gigolo
10 rations = 1 decoration
10 millipedes = 1 centipede
2 snake eyes = 1 paradise
2 wharves = 1 paradox
10-6 phones = 1 microphone
106 phones =1 megaphone
10-2 mental = 1 centimental
10-1 mate = 1 decimate
1012 bulls = 1 terabull
10-12 boos = 1 picoboo
10-15 bismol = 1 femtobismol
1.2 Measurement and Uncertainty
Question 3: How do we represent
precision?
Question 4: How do we determine how
certain we are when taking data?
Measurement = Best Estimate +/- Uncertainty
Or
Examples:
Representing uncertainty:
Absolute or Raw
uncertainty
Percentage
Uncertainty
time = 1.98 0.01 s
time = 1.98 9%
Determining uncertainty with common
measuring devises.
Measurement = Best Estimate +/- Least Count
Determining Uncertainty with common
measuring tools:
Uncertainty isn’t only due to the tool…
* Limitations for the data collector
* YOU decide the uncertainty, but if it is anything other
than the uncertainty of the tool, you must justify your
choice
Ex. The ability to stop a timer the instant a ball rolls past a
given point adds an uncertainty greater than that of the
least count. It’s hard to see just when the ball passes the
point you want. You make a judgment that this additional
uncertainty is perhaps 0.02s. Hense the uncertainty in a
single measurement of the time might be +/-0.03s.
Using a Caliper:
Fig 2 What is the reading that should be recorded
here? Answer: .........
mm
What is the reading that should be recorded here?
Answer: .........
mm
Give a value for the following:
•
•
State which tool you used and why.
State why you chose the uncertainty that you did.
Length of the lab table
Thickness of a 1 zloty coin
The height of your calculator
Question 5: What is the difference
between precision and accuracy?
Precision vs. Accuracy
Accuracy: an indication of how close a measurement
is to the accepted value.
Precision: the degree of exactness to which the
measurement of a quantity can be reproduced (how
close are repeated measurements to each other? If
someone else were to make the same measurement
how close would they be? Often defined by the
tool)
Precision vs. Accuracy
Label each of the ducks with the either:
High
Accuracy, High precision
High Accuracy, Low precision
Low Accuracy, High precision
Low Accuracy, Low precision
Precision vs. Accuracy
Systematic Errors…
Systematic Errors…
Understanding uncertainty and
improving accuracy from random error:
Repeated
Measurements help us
quantify the
uncertainty due to
random error.
Question 7: How do we know what the
uncertainty of a calculation is?
Ex: You have just measured the radius of a ball to
be (6.1 +/- 0.02)mm, but now you want to find the
volume.
4 3
V r
3
Repeated measurements - Averaging
If repeated trials of the same measurement are made, the
greatest deviation from the average of the trials can be
taken as the uncertainty. For example,
Time Trials
2.01
1.82
1.97
2.16
1.94
Adding and Subtracting
An uncertainty range can be found by examining the
minimum and maximum values for the calculated
value.
Ex: Ti = 16 2 oC = 14 to 18 oC
Tf = 34 2 oC = 32 to 36 oC
best value for T = ___________
minimum value for T = ____________
maximum value for T=___________
T = Tf – Ti = ____________
Adding and Subtracting
Shortcut:
Whenever two quantities with uncertainties are
added or subtracted, the uncertainty of the
answer is equal to the SUM of the individual
ABSOLUTE uncertainties.
eg.
T = Tf – Ti
= (34 2 oC) – (16 2 oC)
= (34 – 16 ) (2 + 2) oC
= 18 4 oC
Multiplying and Dividing
An uncertainty range can be found by examining the minimum and maximum
values for the calculated value.
ex.
m = 84.2 0.1 g = 84.1 to 84.3 g
V = 25 2 mL = 23 to 27 mL
Best value for D = m V =
Minimum value for D =
Maximum value for D =
D=
Multiplying and Dividing
Shortcut:
Whenever two quantities with uncertainties are multiplied or divided,
the uncertainty of the answer is equal to the SUM of the individual
PERCENT uncertainties.
Ex.
m
V
D
= 84.2 0.1 g = 84.1 g 0.12%
= 25 2 mL = 25 mL 8%
= (84.1 g 0.12%) (25 mL 8%)
= (84.1 25 g / mL ) (0.12 + 8%)
= 3.364 g / mL 8.12%
= 3.364 0.2732 g / mL
= 3.4 0.3 g / mL
You try:
The lengths of the sides of a rectangular plate are
measured. The width is (50+/-1)mm and the length
is (25 +/- 1)mm. What is area (with uncertainty) of
the plate.
Find the area of the top of your lab table. Report
your answer with uncertainties. Show all
measurements and calculations.
Power Functions
Power
functions are
just like
multiplication!
Other Functions
If the calculation involves mathematical operations other than + , - , or (eg.
root functions, trigonomeric functions, logarithmic functions, … ), then the
short cuts do not apply and we must find the minimum and maximum
values and use the greatest deviation from the best value as the
uncertainty.
ex.
= 33C 2C = 31C to 35C
best value for sin = sin(33) =
minimum value for sin = sin(31) =
maximum value for sin = sin(35) =
Take the maximum: sin =
Volume of a sphere
Ex: You have just measured the radius of a ball to
be (6.1 +/- 0.02)mm, but now you want to find the
volume.
4 3
V r
3
You try:
The power dissipated in a resistor of resistance R
carrying a current I is equal to I^2R. The value of I
has an uncertainty of +/- 2% and the value of R
has an uncertainty of +/-10%. The value of the
uncertainty in the calculated power dissipation is: