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Physics 201 –College Physics
Akhdiyor Sattarov
Lectures MWF 1:50-2:40
E-mail [email protected]
Phone: 458-7967 office / 845-6015 lab
Office Hours: ? or by appointment,
Office: MPHYS 303
Web-site: http://people.physics.tamu.edu/a-sattarov/
• Text: Physics 8th ed by Young & Geller with Mastering Physics; PHYS 202 Lab Manual
• Optional: Student Solutions Manual, Student Student Guide• • Grading: 4 exams 60%; Final (comprehensive) 20%; Lab10%; Recitation
5%; Homework (Mastering Phys) 5%• You must achieve 70% or better in the laboratory in order to pass the course.• If your grade on the Final Exam is higher than your lowest grade on one of
the four exams during the semester, your grade on the Final will replace that one lowest exam grade in computing the course grade.
• Sept. 3 is last day to drop with no record. • Nov. 5 is the last day to Q-drop. • Final Exam is December 14 2010 3:30pm-5:30pm
• To provide understanding of the physical world by developing theories based on experiments
• Physical theories model real world and are statement of what has been observed and provide prediction of new observations that can be confirmed or turned down by experiment
• Broad and solidly established by experiment physical theory – physical law
Physical Law• True, there is no contradiction to observation• Universal – apply everywhere in the universe• Simple• Stable – unchanged since first discovered
The Goal of Physics
How do we analyze physical system? • Simplification of a complicated system – depending on our goals we
exclude/neglect unimportant/weak effects – isolate system of interest.
Example: A small rock thrown upward – we can neglect the air resistance
• Very often we use point particle – idealized object that lacks spatial extensions
Example: Earth orbiting around Sun, we can treat Earth as point particle because the radius of Earth much smaller than the dimensions of the system
Standards and Units• Physical quantity - Quantity used to describe an observation of
physical phenomenon • Each physical quantity is represented with respect to reference
standard – Unit of the quantity• Some Physical quantities are defined only by describing a
procedure for measuring them – operational definition• Some physical quantities can be derived from other quantities• Most fundamental quantities:
International System Length meter=distance traveled in vacuum by light
during 1/299792458 of secTime second-9,192,631700 times the period of oscillations of radiation from the cesium atom.Mass kilogram=90% Platinum 10% iridium alloy cylinder
h=d=0.03917m
Since we will work with very small and very big systems we have to have conversion multipliers
Power of 10 Prefix Abbreviation
10-6 micro- m 10-3 milli- m 10-2 centi- c 103 kilo- k 106 mega- M 109 giga- G
Using prefixes• 1cm=1 centimeter=1x10-2m=0.01m – thickness of a notebook
• 1fm=1 femtometer=10-15m – radius of a nucleus
• 1ns=1 nanosecond=10-9s – time required for light to travel about 1ft.
• 1ms=1 millisecond=10-3s - time required for sound to travel about 1ft.
• 1kg=1 kilogram=103g
• 1Mg=1000kg=106g – mass of water that has volume of 1m3 at 4oC
Dimensional analysis
In Physics, the word dimension denotes the physical nature of a quantity
Example: distance between 2 points can be measured in meters, centimeters, feet etc. – different ways of expressing the dimension of length
• it is often necessary to derive mathematical expression or equation or check its correctness. A useful procedure for doing this is called dimensional analysis.
• Dimensional analysis makes use of the fact that dimensions can be treated as algebraic quantities
Example: Volume of a cube of water, L=2mExample: Find mass of water, density of water 997 kg/m3
Example: Express speed of light 3x108 m/s in km/h
38222222 mmmmmmmLLLV
kgmmkgm
mkgVm 797689978997 3
33
3
hkm
hs
mkm
sm
smc 988 1008.13600
1000103103
Always use units in calculations!
You can not add or subtract quantities that have different units
It will help you to check dimensional consistency of your result!!
3kg+15m means something is wrong
Mass=r2*V=(997kg/m3)2 8m3= ****** kg2/m3 - something is wrong
Precision and Significant figures
• No physical quantity can be determined with complete accuracy• Knowing experimental uncertainties in any measurements is very
important• Accuracy of measurements depends on the sensitivity of the
devices, the skill of the investigator…• In many cases result from one measurement is used in derivation of
other physical quantities
We have to develop basic and reliable method of keeping track of those uncertainties in subsequent calculations.
Example: Let we have to measure area of a rectangular plate with a meter stick. Suppose that we can measure particular side with 0.1cm accuracy. Suppose that side a=16.3cm and side b=4.5cm.
• Side a=16.3+/-0.1 cm, side b=4.5+/-0.1cm• Mid Area=16.3cm x 4.5cm = 73.35cm2
• High Area=16.4cm x 4.6cm = 75.44cm2
• Low Area=16.2cm x 4.4cm = 71.28cm2
so our area 73+/-2cm – note that the answer has two significant figuresIn our example First term had 3 and the second 2 significant figures
In multiplying (dividing) two or more quantities, the number of significant figures in the final result is no greater than the number of significant figures in the term that had fewest significant figures.
In addition (subtraction) two or more quantities the final result can have no more decimal places than the term with fewest decimal places
Example: 128.???+5.35?=133.???
Scalar and vector• Scalar physical quantity is a quantity described by single
number, examples are time, mass, density, charge etc. • Vector quantity is a quantity that is described by a
magnitude and a direction. • Graphically vector is represented as an arrow pointing in
given direction and having length that is proportional to the magnitude of the vector.
• Symbolically vector is represented by a label with small arrow sign over it.
• Example: Position vector – shows a direction and how far from the reference point the object resides.
• Example: Displacement vector– shows change in position, from starting point to final
A
D
B
Let have several vectors
C E
We say that vectors are parallel
We say that vectors are antiparallel
We say that A=D
We say A=-E
Product of a scalar and a Vector
Resulting Vector is collinear (parallel or anti parallel) to the original vector.
Adding vectors: Tail to tip method
ABBA
A
B
A+B B+A=
•Draw the vectors, with proper scaling
•Draw the second one putting its tail to the tip of the first one
•Draw the resultant from the tail of the first vector to the tip of the second
•One can change the order of the vectors
Parallelogram method
A
B
2 vectors are along two sides of a parallelogram
Resulting vector along the diagonal of the parallelogram that starts at the tails of the vectors
A
B
A+B
Multiplying sum of two vectors by scalar
(A+B)*ss.A
s.B
Using two similar triangles, we find that the bigger triangle is just scaled by s.
BsAsBAs
)(
Subtraction of vectors
CBBA
AAA
ˆ
Direction vector
Note:
It is in the direction of the vector A, but has a unit length and it is dimensionless.
AAA ˆ
Components of vectors (2d)• Let we have some vector• We define some reference frame• A tail of the vector positioned at O.• Define two component vectors:
yx AAA
x
yA
Ax
Ay
QAy – y-component of vector A
Ax – x-component of vector A
Components are not vectors
They can be positive and negative, depending on an angle
y
x
yx
yxyx
yy
xx
AA
AAA
AAAorAAAAA
AAorAA
AAorAA
tan
sin,cos,
90sinsin,0,0
0cos0,cos0,
22
Let define angle between vector and positive x-direction
Ay=IAI sin
Ax=IAI cosA vector can be represented in 2 ways
a) by its components
b) By its magnitude and angle with positive x-direction (in 3d case also angle with positive z-direction)
Example: A person starts from point A and arrives at point B. Find components, magnitude of the position vectors and angle between the vector and x-axis. Find the displacement vector.
5.1tantan 11 x
yA A
A
A
B
X (km)
Y (km)
A
Ax=2km
Ay=3km
Bx=-2km
By=-1km5.0tantan 11
x
yB B
B
B
QAQB
Pay attention!! You may get this angle
Multiplication by a scalar and addition of vectors becomes very simple
As
BA
As
yyxx BABA ,
22 )()( yx AsAs As
)( 222yx AAs
yx AsAs ,
x-componet y-componet
x-componet y-componet
Example 1.45: Vector A has components Ax=1.3cm, Ay=2.25cm; vector B has components Bx=4.1cm and By=-3.75cm. Find the components of the vector sum A+B;The magnitude and direction of A+B;The components of the vector difference B-A;The magnitude and direction of B-A;
Example1.50 A postal employee drives a delivery truck along the route shown in figure below. Use components to determine the magnitude and direction of the truck’s resultant displacement. Then check the reasonableness of your answer by sketching a graphical sum.
Kinematics – describes the motion of object without causes that leaded to the motion
We are not interested in details of the object (it can be car, person, box etc..). We treat it as dimensionless point
We want to describe position of the object with respect to time – we want to know position at any given time
Path (trajectory) – imaginary line along which the object moves
Motion along a straight line• We will always try to set up our reference frame in a such
way that motion is along or “x” or “y” coordinate axis. The direction of the axis is up to us.
• Position vector then can be represented by a single component, the other components are equal to zero.
r(t1)r(t2)r(t3)
x
y
t=t1 t=t2 t=t3
x1=19m,t1=1sx2=277m,t1=4s
),,()( 2222 zyxtr
011 zy
022 zy
),,()( 1111 zyxtr
Very often I will write rn instead of r(tn), the same for the components of the vector, for example, yn instead of y(tn)