Physics and Measurement (1)
Here we learn the language and the tools of physics.
Mr. KlapholzShaker Heights
High School
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.
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
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
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
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.
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.
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.
Accuracy vs. Precision (1 of 2)
http://www.wellesley.edu/Chemistry/Chem105manual/Lab04/AccuracyPrecision.jpg
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.
Uncertainties in Data Tablesare often shown as column headings
Time / s± 0.2
Position / m± 0.3
0.0 1.40.9 2.5
Uncertainties are shown on a graph using “error bars” (or boxes).
https://www.graphpad.com/faq/viewfaq.cfm?faq=106
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
“Vectors” are quantities that do have direction. Examples:
• Velocity• Acceleration• Force• Momentum
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.
Adding Vectors: A + B = C
http://img.sparknotes.com/content/testprep/bookimgs/sat2/physics/0011/parallelogram_2.gif
Calculating the components of vectors
http://www.niiler.com/phy130/vector3.png
Use ‘sin’ for oppositeUse ‘cos’ for adjacent