The Nature of Measurement : The Nature of Measurement The SI system of fundamental and derived units
Uncertainty and error in measurement 8/26/2011 1 AP Physics - Intro to AP Physics
The Nature of Measurement : The Nature of Measurement Consider the following reading on a meter stick: cm 1 2 3 4 5 6 7 8 8/26/2011 2 AP Physics - Intro to AP Physics
Why do we measure? : Why do we measure? Physics is concerned with the description and understanding of nature, and measurement is one of its most important tools.
Measurements concretely communicate quantity. 8/26/2011 3 AP Physics - Intro to AP Physics
Base (or fundamental) Units of Measure : Base (or fundamental) Units of Measure These seven units measure fundamental physical properties of nature.
They are not composed of other units.
meter (m), a measure of length
kilogram (kg), a measure of mass
seconds (s), a measure of time
ampere (A), a measure of electric current
kelvin (K), a measure of temperature
mole (mol), a measure of amount of substance
candela (cd), a measure of luminous intensity 8/26/2011 4 AP Physics - Intro to AP Physics
1. Length : 1. Length the meter (m)
1 m = the distance traveled by light in a vacuum in a time of 1/299,792,458 s.
Common measuring instruments:
Meter stick, tape measure 8/26/2011 5 AP Physics - Intro to AP Physics
2. Mass : 2. Mass the kilogram (kg)
1 kg = the mass of a certain quantity of a platinum-iridium alloy kept at the Bureau International des Poids et Mesures in France
Common measuring instruments:
Scale, Ohaus balance 8/26/2011 6 AP Physics - Intro to AP Physics
3. Time : 3. Time the second (s)
1 s = the duration of 9,192,631,770 full oscillations of the electromagnetic radiation emitted in a transition between the two hyperfine energy levels in the ground state of a cesium-133 atom.
Common measuring instrument:
Stopwatch 8/26/2011 7 AP Physics - Intro to AP Physics
Derived Units : Derived Units these units are composed of other units
examples:
velocity = m/s
power = watts (kg m2 s-3 or kg m2/s3 ) 8/26/2011 8 AP Physics - Intro to AP Physics
Derived Units : Derived Units For our study of dimensional analysis, recall the following quantities that are measured in derived units:
area (m2)
volume (m3)
velocity (m/s)
acceleration (m/s2) 8/26/2011 9 AP Physics - Intro to AP Physics
Dimensional Analysis : Dimensional Analysis How many meters tall are you?
Find a conversion factor to get you from your current units to your desired units.
1 meter = 39.37 inches
Use the equation to create a fraction equal to 1. Put the unit you are converting TO on TOP and converting FROM on the BOTTOM.
39.37 inches/1 meter
Multiply the original value by the fraction. 8/26/2011 10 AP Physics - Intro to AP Physics
Dimensional Analysis : Dimensional Analysis Practice 8/26/2011 11 AP Physics - Intro to AP Physics
Consistency of Units : Consistency of Units Equations must result in the same units on both sides of equation.
Example:
Formula for period of a pendulum
T = 2π √(l/g)
T = period (s)
l = length (m)
g = gravitational acceleration (m/s2)
Reduces into seconds on both sides!!! 8/26/2011 12 AP Physics - Intro to AP Physics
Stop to Think… : Stop to Think… Are the following measured in fundamental or derived units?
Area of a football field
Distance from Earth to the Sun
Acceleration due to gravity on Mars
Period of rotation of Mars
Velocity of a coconut-carrying swallow
Mass of above-mentioned coconut
Weight of above-mentioned coconut
Luminous intensity of the Griswold Family Christmas Exterior Illumination
Power used by the Griswold Family Christmas Exterior Illumination 8/26/2011 13 AP Physics - Intro to AP Physics
Scientific Notation : This number becomes the exponent of ten. Moving the decimal left makes it positive, right makes negative. Scientific Notation Is there an easier way to express large numbers?
Ex) 23,471,693,273 . 2 3471693273 Move the decimal point so that there is only one non-zero digit on the left of it. Count the number of decimal places you moved the decimal point. x 10 10 10 8/26/2011 14 AP Physics - Intro to AP Physics
Stop to Think… : Stop to Think… Place the following numbers into scientific notation.
93,000,000
3,600
0.00015
0.453
152
63
9 8/26/2011 15 AP Physics - Intro to AP Physics
Metric Prefixes : Metric Prefixes * rarely used 8/26/2011 16 AP Physics - Intro to AP Physics
Stop to Think… : Stop to Think… Use scientific notation and metric prefixes to state the given measurements in a briefer expression. 8/26/2011 17 AP Physics - Intro to AP Physics
Precision vs. Accuracy : Precision vs. Accuracy Accuracy is how close readings or calculations are to the true or accepted value.
Precision is how many decimal places an instrument resolves.
To illustrate this…. a challenge of archery!!!! 8/26/2011 18 AP Physics - Intro to AP Physics
Precision vs. Accuracy : Precision vs. Accuracy x x x x x x x Precise, but not accurate! 8/26/2011 19 AP Physics - Intro to AP Physics
Precision vs. Accuracy : Precision vs. Accuracy x x x x x x x x Accurate, but not precise! 8/26/2011 20 AP Physics - Intro to AP Physics
Precision vs. Accuracy : Precision vs. Accuracy x x x x x x x Neither accurate nor precise! 8/26/2011 21 AP Physics - Intro to AP Physics
Precision vs. Accuracy : Precision vs. Accuracy x x x x x x x Both accurate and precise! 8/26/2011 22 AP Physics - Intro to AP Physics
Stop to Think… : Stop to Think… Which is more precise, the metric side of a meter stick or the inches side?
What could affect the accuracy of a meter stick? 8/26/2011 23 AP Physics - Intro to AP Physics
Significant Figures : Significant Figures Think about our definition of precision…
I want to measure a mile with a meter stick…
Does it make sense to record to the millimeters place if I haphazardly measured a mile?
The number of significant digits clues you in to the precision of the measurement. 8/26/2011 24 AP Physics - Intro to AP Physics
How many decimal points do I record? : How many decimal points do I record? Always all the measured digits, and one estimated
For graduated instruments (meter stick, spring scales)
Record to half the smallest marking (estimate 0.5 mm on a meter stick)
For digital instruments
Record the measurement given, exactly as it is shown
ex) If a digital scale reads 1.600 g, then record 1.600 g, not 1.6 g. 8/26/2011 Intro to Physics: Scientific Inquiry 25
Sig Fig Rules : Sig Fig Rules 1. When multiplying and dividing quantities, leave (round to) as many significant figures in the answer as there are in the quantity with the least number of significant figures.
Ex) 5.6 x 4.687985
Calculator reports = 26.252716
Best reliable answer: 26 8/26/2011 26 AP Physics - Intro to AP Physics
Sig Fig Rules : Sig Fig Rules 2. When adding or subtracting quantities, leave the same number of decimal places (rounded) in the answer as there are in the quantity with the least number of decimal places.
Ex) 5.6 + 4.687985
Calculator reports = 10.287985
Best reliable answer: 10.3 8/26/2011 27 AP Physics - Intro to AP Physics
When are digits significant? : When are digits significant? 1. Zeros at the beginning of a number are not significant. They merely locate the decimal point.
2. Zeros within a number are significant.
3. Zeros at the end of a number after the decimal point are significant.
4. In whole numbers without a decimal point that end in one or more zeros (trailing zeros), the zeros may or may not be significant. 8/26/2011 AP Physics - Intro to AP Physics 28
Error vs. Uncertainty : Error vs. Uncertainty Are they the same thing?
Error:Accuracy::Uncertainty:Precision 8/26/2011 29 AP Physics - Intro to AP Physics
Error : Error Random
can be reduced with repeated readings
Systematic
cannot be reduced with repeated readings 8/26/2011 30 AP Physics - Intro to AP Physics
How to state uncertainties : How to state uncertainties Absolute
Fractional
Percentage 8/26/2011 31 AP Physics - Intro to AP Physics