physics and measurement (1) here we learn the language and the tools of physics. mr. klapholz shaker...

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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