Physics 201 General Physics · · 2009-09-11Physics 201 General Physics Prof. Susan Coppersmith...

Physics 201 General Physics

Prof. Susan Coppersmith Prof. Albrecht Karle

Course information

•  Course homepage •  Let’s have a quick look: •  http://www.physics.wisc.edu/undergrads/courses/

fall09/201/ –  Find there detailed information on syllabus, homework,

exams, grading, discussion, labs •  Syllabus:

–  Lectures: Typically 1 Chapter per week from textbook –  Two discussion sessions –  One Lab –  One homework (Always due on Thursdays)

Textbook, e-book and WebAssign

•  The textbook is available in electronic form as an e-book. –  Paul Tipler and Gene Mosca, Physics for Scientists and

Engineers, 6th ed. –  You can read it from any computer with access to

internet. http://webassign.net/login.html. –  This is by far the cheapest solution. If you like to buy it in real

paper, it is also available as softcover in 2 volumes (this course covers the 1st volume)

•  WebAssign: –  This is our homework assignment system. Problems are taken from the

textbook but numbers are randomized. –  Let’s have a quick look into WebAssign: –  Intro to WebAssign –  Student Guide to WebAssign

©2008 by W.H. Freeman and Company

Discussions, Labs TA’s

Our team of Teaching Assistants will be your instructors in discussions and labs:

Sections Your TA -------------------------------- •  301 302 Eunsong Choi •  303 309 Jialu Yu •  304 310 Jared Schmitthenner •  305 311 Andrew Long •  306 307 Daniel Schroeder

Office hours Monday 4:20pm – 5:10pm Jared Tuesday 10:45am – 11:45am Prof. Coppersmith 11am – 11:50am Dan 1:20pm – 2:10pm Jialu 2:25pm – 3:15pm Andrew Wednesday 11am – 11:50am Eunsong 4:20pm – 5:10pm Jared Thursday 11am – 11:50am Dan - 12:05pm – 12:55pm Eunsong 1:20pm – 2:10pm Jialu 2:25pm – 3:15pm Andrew 2:30pm – 3:30pm Prof. Karle (best by appointment)

Nature of Science - Theory and observation Theories are made to explain observations.

Theories will make predictions, (so that they are testable).

Observations and experiments are used to test if the prediction is accurate.

The cycle continues.

In history, physics and astronomy, have set the ground rules of modern science.


Example: Determination of the Earth diameter by Eratosthenes (276 BC– 195 BC)

•  Eratosthenes wanted to determine the diameter of the Earth. (Yes, the standard model at the time was that the Earth was round – that was not the question.)

•  He observed the angle of the sun at the same time in Alexandria and some 800km South of Alexandria (Syene= Aswan)

•  From the difference, he was able in inclination, records indicate that he was able to determine the Earth’s diameter to within 2% precision.

•  An example of great science!

Example: Determination of the Earth diameter by Eratosthenes (276 BC– 195 BC)

•  Eratosthenes wanted to determine the diameter of the Earth. (Yes, the standard model at the time was that the Earth was round – that was not the question)

•  He observed the angle of the sun at the same time in Alexandria and some 800km South of Alexandria (Syene= Aswan)

•  From the difference, he was able in inclination, records indicate that he was able to determine the Earth’s diameter to within 2% precision.

•  An example of great science!

Units •  Physical quantities have units! •  Example: Unit of length

–  Eratosthenes used the unit stadion. (The hellenic stadion was pretty big: 185m)

–  In the Middle ages many kingdoms had different definitions of a foot, etc.

•  Today, the scientific community uses the SI system of units. There are 7 basic units, such as –  Length: Meter (Based on the speed of light: length of path

traveled by light in 1/299,792,458s) –  Mass: kg (Platinum cylinder in International Bureau of Weights

and Measures, Paris) –  Time: s (Time required for 9,192,631,770 periods of

radiation emitted by cesium atoms.)

SI Units

SI Base quantities

Length meter m

Time second s

Mass kilogram kg

Electric Current ampere A

Temperature kelvin K

Amount of substance mole mol

Luminous intensity candela cd


Prefixes •  Depending on the

scale one often likes to use prefixes.

•  Example, for length it is convenient to use km = 1000m when traveling by car, or nm=10^-9m when discussing molecular scale objects.

Conversions •  Conversions between units are very helpful. The use of different

units has again and again lead to errors, sometimes with bad consequences.

•  The conversion of units is also a frequent source of errors engineering and science (and exams).

•  But it is easy to avoid.

•  Avoid skipping the units (for example because it is less writing time) –  Are all the ingredients for a problem in the same units? If not, it is good

practice to perform the conversion, before doing any algebra. –  Basic SI units are always safe –  It is OK to us km or nm, but need to take care that you don’t mix m and km –  Develop good practice.

•  We will expect that you give results with units, also in exams.

Derived quantities and dimensions

m2

m3

m/s

m/s2 N=kg•m/s2 N/m2=kg/m•s2 kg/m3 …

Measurement and Significant figures •  A measurement has a precision (or error). •  Measurement of the distance Earth – moon with laser pulse based

on travel time of light. Error: a few cm! (position of the mirror) •  What is the relative error?

The Greek astronomer Hipparch, ~200BC determined the distance of the moon to about ~70 Earth diameters, 5% precision, not too bad.

Measurement and Significant figures

•  A measurement has a precision (or error). •  Significant figures reflect the precision of the measurement.

Example: •  Pocket calculator •  whiteboard, •  WebAssign intro

Measurement and Significant figures

•  Calculators will not give you the right number of significant figures; they usually give too many but sometimes give too few (especially if there are trailing zeroes after a decimal point).

•  The top calculator shows the result of 2.0 / 3.0.

•  The bottom calculator shows the result of 2.5 x 3.2.


The universe by orders of magnitude

A quick way to estimate a calculated quantity is to round off all numbers to one significant figure and then calculate. Your result should at least be the right order of magnitude; this can be expressed by rounding it off to the nearest power of 10.

Such back on the envelope estimates are very helpful for double checking a result of a calculation.

Diagrams are also very useful in making estimations.

Order of magnitude: Rapid Estimating


Tire treads


How many grains of sand on a beach?

Phys201Fall2009

Tuesday,September8,2009

Chapter1:Measurementandvectors

ReviewfromlastDme:converDngunits

•  UnitsineveryequaDonhavetomatch!ItisaverygoodideatokeepunitsaswellasnumberswhensolvingequaDons.

Thedensityofseawaterwasmeasuredtobe1.07g/cm3.ThisdensityinSIunitsis

A.  1.07kg/m3

B.  (1/1.07)×103kg/m3

C.  1.07×103kgD.  1.07×10–3kg

E.  1.07×103kg/m3

IfKhasdimensionsML2/T2,thekinK=kmv2must

A.  havethedimensionsML/T2.

B.  havethedimensionM.

C.  havethedimensionsL/T2.

D.  havethedimensionsL2/T2.

E.  bedimensionless.

Vectors•  Inonedimension,wecanspecifydistancewitharealnumber,including+or–sign.

•  Intwoorthreedimensions,weneedmorethanonenumbertospecifyhowpointsinspaceareseparated–needmagnitudeanddirecDon.

Madison, WI and Kalamazoo, MI are each about 150 miles from Chicago.

DenoDngvectors

•  Twoofthewaystodenotevectors:– BoldfacenotaDon:A– “Arrow”notaDon:

€

A

©2008by W.H. Freeman and Company

Displacementisavector


Addingdisplacementvectors


“Head‐to‐tail”methodforaddingvectors


VectoraddiDoniscommutaDve


Addingthreevectors:vectoraddiDonisassociaDve.


Avector’sinversehasthesamemagnitudeandoppositedirecDon.


SubtracDngvectors

Example1‐8.Whatisyourdisplacementifyouwalk3.00

kmdueeastand4.00kmduenorth?



Componentsofavector


Componentsofavectoralongxandy


MagnitudeanddirecDonofavector


Addingvectorsusingcomponents

Cx = Ax + Bx Cy = Ay + By


Unitvectors

A unit vector is a dimensionless vector with magnitude exactly equal to one.

The unit vector along x is denoted The unit vector along y is denoted The unit vector along z is denoted

WhichofthefollowingvectorequaDonscorrectlydescribestherelaDonshipamongthevectorsshowninthefigure?

correct. istheseofNone.E0.D

0.C

0.B

0.A

=++

=−−

=+−

=−+

CBA

CBA

CBA

CBA

Canavectorhaveacomponentbiggerthanitsmagnitude?

Yes

No

Canavectorhaveacomponentbiggerthanitsmagnitude?

• Yes

• No

The square of a magnitude of a vector R is given in terms of its components by

R2 = Rx2 + Ry

2 .

Since the square is always positive, no component can be larger than the magnitude of the vector.


ProperDesofvectors:summary

Physics 201 General Physics · · 2009-09-11Physics 201 General Physics Prof. Susan Coppersmith...

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