Physics 201 General Physics

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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.

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 Tuesday 10:45am – 11:45am 11am – 11:50am 1:20pm – 2:10pm 2:25pm – 3:15pm Wednesday 11am – 11:50am 4:20pm – 5:10pm Thursday 11am – 11:50am 12:05pm – 12:55pm 1:20pm – 2:10pm 2:25pm – 3:15pm 2:30pm – 3:30pm (best by appointment)

Jared Prof. Coppersmith Dan Jialu Andrew Eunsong Jared Dan Eunsong Jialu Andrew Prof. Karle

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. ©2008 by W.H. Freeman and Company

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

©2008 by W.H. Freeman and Company

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

©2008 by W.H. Freeman and Company

Order of magnitude: Rapid Estimating 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.

Tire treads

©2008 by W.H. Freeman and Company

©2008 by W.H. Freeman and Company

©2008 by W.H. Freeman and Company

©2008 by W.H. Freeman and Company

How many grains of sand on a beach?

©2008 by W.H. Freeman and Company

Phys
201
 Fall
2009
 Tuesday,
September
8,
2009
 Chapter
1:

Measurement
and
 vectors


Review
from
last
Dme:
converDng
 units
 •  Units
in
every
equaDon
have
to
match!

It
is
a
 very
good
idea
to
keep
units
as
well
as
 numbers
when
solving
equaDons.


The
density
of
seawater
was
measured
to
 be
1.07
g/cm3.

This
density
in
SI
units
is
 A.  B.  C.  D.  E. 

1.07
kg/m3

 (1/1.07)
×
103
kg/m3


 1.07
×
103
kg
 1.07
×
10–3
kg
 

 1.07
×
103
kg/m3



The
density
of
seawater
was
measured
to
 be
1.07
g/cm3.

This
density
in
SI
units
is
 A.  1.07
kg/m3

 B.  (1/1.07)
×
103
kg/m3


 C.  1.07
×
103
kg
 D.  1.07
×
10–3
kg
 

 E.  1.07
×
103
kg/m3



If
K
has
dimensions
ML2/T2,
the
k
in
K
=
 kmv2
must
 A.  B.  C.  D.  E. 

have
the
dimensions
ML/T2.

 have
the
dimension
M.


 have
the
dimensions
L/T2.
 have
the
dimensions
L2/T2.
 

 be
dimensionless.




If
K
has
dimensions
ML2/T2,
the
k
in
K
=
 kmv2
must
 A.  have
the
dimensions
ML/T2.

 B.  have
the
dimension
M.


 C.  have
the
dimensions
L/T2.
 D.  have
the
dimensions
L2/T2.
 

 E.  be
dimensionless.




Vectors
 •  In
one
dimension,
we
can
specify
distance
 with
a
real
number,
including
+
or
–
sign.
 •  In
two
or
three
dimensions,
we
need
more
 than
one
number
to
specify
how
points
in
 space
are
separated
–
need
magnitude
and
 direcDon.
 Madison, WI and Kalamazoo, MI are each about 150 miles from Chicago.

DenoDng
vectors
 •  Two
of
the
ways
to
denote
vectors:
 – Boldface
notaDon:

A
  – “Arrow”
notaDon:


A



Displacement
is
a
vector


©2008
by W.H. Freeman and Company


Adding
displacement
vectors


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by W.H. Freeman and Company


“Head‐to‐tail”
method
for
adding
vectors


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by W.H. Freeman and Company


Vector
addiDon
is
commutaDve


©2008
by W.H. Freeman and Company


Adding
three
vectors:
 vector
addiDon
is
associaDve.


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by W.H. Freeman and Company


A
vector’s
inverse
has
the
same
 magnitude
and
opposite
direcDon.


©2008
by W.H. Freeman and Company


SubtracDng
vectors


©2008
by W.H. Freeman and Company


Example
1‐8.


 What
is
your
displacement
if
you
walk
3.00
 km
due
east
and
4.00
km
due
north?


©2008
by W.H. Freeman and Company


Components
of
a
vector


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by W.H. Freeman and Company


Components
of
a
vector
along
x
and
y


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by W.H. Freeman and Company


Magnitude
and
direcDon
of
a
vector


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by W.H. Freeman and Company


Adding
vectors
using
components


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by W.H. Freeman and Company


Cx = Ax + Bx Cy = Ay + By

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

©2008
by W.H. Freeman and Company


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

Which
of
the
following
vector
equaDons
 correctly
describes
the
relaDonship
among
 the
vectors
shown
in
the
figure?



A. B. C. D.

   A+ B −C =0    A− B +C =0    A− B −C =0    A+ B +C =0

E. None of these is correct.

Which
of
the
following
vector
equaDons
 correctly
describes
the
relaDonship
among
 the
vectors
shown
in
the
figure?



A. B. C. D.

   A+ B −C =0    A− B +C =0    A− B −C =0    A+ B +C =0

E. None of these is correct.

Can
a
vector
have
a
component
 bigger
than
its
magnitude?
 Yes No

Can
a
vector
have
a
component
 bigger
than
its
magnitude?
 • Yes • No The square of a magnitude of a vector R is given in terms of its components by R2 = Rx2 + Ry2 . Since the square is always positive, no component can be larger than the magnitude of the vector.

ProperDes
of
vectors:
summary


©2008
by W.H. Freeman and Company