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

“Scalars” are quantities that do not have direction. Examples:

• Time• Mass• Energy• Temperature

“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

Components of vectors

http://www.phys.unsw.edu.au/PHYS1169/beilby/vectors.html

Calculating the components of vectors

http://www.niiler.com/phy130/vector3.png

Use ‘sin’ for oppositeUse ‘cos’ for adjacent

Get magnitude from components using Pythagorean theorem:

A2 = Ax2 + Ay

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