Physics 201 –College Physics

Akhdiyor Sattarov

Lectures MWF 1:50-2:40

E-mail a-sattarov@physics.tamu.edu

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

r

AA

Magnitude of a vector

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

)(

CBACBA

)()(A

B

C

CBA

)(

CB

Sum of 3 vectors

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

x

t

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)

Motion along a straight line• x component of a displacement vector – for time

interval t1 t2 is equal Dx=x2-x1

• Note that we can define another reference frame, position vector will be different in each frame, not a displacement vector

r(t1)r(t2)

x

y

12 rrd

12 '' rrd

r’ 1

r’ 2

x’y’