physics and measurement (1)
DESCRIPTION
Mr. Klapholz Shaker Heights High School. Physics and Measurement (1). Here we learn the language and the tools of physics. Magnitude. The mass of the universe is about 1 x 10 50 kg. Even though this is a very large mass, we have no trouble writing it in scientific notation. - PowerPoint PPT PresentationTRANSCRIPT
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Physics and Measurement (1)
Here we learn the language and the tools of physics.
Mr. KlapholzShaker Heights
High School
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Magnitude
• The mass of the universe is about 1 x 1050 kg. Even though this is a very large mass, we have no trouble writing it in scientific notation.
• The mass of an electron: 10-30 kg.• How much more massive is the universe than
the electron? (Please use your calculator).• 1x1050 kg / 1x10-30 kg = 1080 • What are the units? Notice again how easily
scientific notation let’s us deal with this.
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Fundamental UnitsIdea Unit Symbol
Length meter m
Mass kilogram kg
Time second s
Electrical current ampere A
Temperature Kelvin K
Amount of matter mole mol
Intensity of light candela cd
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Some Derived SI UnitsIdea Unit Symbol
Speed meter / second m s-1
Force Newton N = kg m s-2
Energy Joule J = kg m2 s-2
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Significant Figures• This is a system of honestly reporting a value, but
not claiming to know more than we do know.• For example, if the edge of a cube is 1.2 cm, then
what is its volume? V = L3 = (1.2)3 = 1.728 cm3.• But wait, it is not honest to start with 2 digits,
and end up with 4 digits. So, V = 1.7 cm3.• The I.B.O. allows us to disagree by one significant
figure without being penalized.• We will explore this more in the Problem Solving
section
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Uncertainty and Error
• No measurement is perfect.• “Random” errors make a measurement too
great as often as they make it too small. One way to cope is to repeat the measurement many times.
• “Systematic” errors tend to make the measurement either always too great or too small. One way to cope is to make the same measurement using a different method.
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Uncertainty and Error• If you use a ruler to measure the width of a piece of
printer paper, you would notice that it is about 21.00 cm.
• Often we take the uncertainty to be half of the smallest division. Since the markings on the ruler show every millimeter, (10 mm = 1 cm), it would be reasonable to say that the uncertainty (the error) in our measurement was about 0.5 mm.0.5 mm = 0.05 cm.
• So the width of the paper is 21.00 ± 0.05 cm.• This means that most likely, the width of the paper
is between 20.95 and 21.05 cm.
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Examples of Errors
• Examples of Random Errors:– Unpredictable changes in room temperature.– Variation among items that were supposed to be
identical.• Examples of Systematic Errors:– Doing an experiment outdoors as the sun heats up
the apparatus. – Not ‘zeroing’ a balance.
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Accuracy vs. Precision (1 of 2)
http://www.wellesley.edu/Chemistry/Chem105manual/Lab04/AccuracyPrecision.jpg
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Accuracy vs. Precision
• “Accuracy” describes how close a measurement comes to the ‘true’ value.
• “Precision” describes how closely a group of measurements agree with each other.
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Uncertainties in Data Tablesare often shown as column headings
Time / s± 0.2
Position / m± 0.3
0.0 1.40.9 2.5
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Uncertainties are shown on a graph using “error bars” (or boxes).
https://www.graphpad.com/faq/viewfaq.cfm?faq=106
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Slope (“gradient”) and y-intercept have uncertainties. Draw the best line and
the “extreme lines”.
http://w3eos.whoi.edu/12.747/notes/lect03/egspan.gif
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“Scalars” are quantities that do not have direction. Examples:
• Time• Mass• Energy• Temperature
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“Vectors” are quantities that do have direction. Examples:
• Velocity• Acceleration• Force• Momentum
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When we handwrite the symbol of a vector, we put an arrow over it.
When we type the symbol of a vector, we use bold.
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Adding Vectors: A + B = C
http://img.sparknotes.com/content/testprep/bookimgs/sat2/physics/0011/parallelogram_2.gif
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Components of vectors
http://www.phys.unsw.edu.au/PHYS1169/beilby/vectors.html
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Calculating the components of vectors
http://www.niiler.com/phy130/vector3.png
Use ‘sin’ for oppositeUse ‘cos’ for adjacent
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Get magnitude from components using Pythagorean theorem:
A2 = Ax2 + Ay
2