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Page 1: Dimensi Dan Satuan

Physics 111: Lecture 1, Pg 1

Physics 111: Lecture 1Physics 111: Lecture 1“Mechanics for Physicists and Engineers”“Mechanics for Physicists and Engineers”

Agenda for TodayAgenda for Today

AdviceAdvice Scope of this courseScope of this course Measurement and UnitsMeasurement and Units

Fundamental unitsSystems of unitsConverting between systems of unitsDimensional Analysis

1-D Kinematics (review)1-D Kinematics (review)Average & instantaneous velocity and accelerationMotion with constant acceleration

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Physics 111: Lecture 1, Pg 2

Course Info & AdviceCourse Info & Advice

See info on the World Wide Web (heavily used in Physics 111)Go to http://www.physics.uiuc.edu and follow “courses” link to the

Physics 111 homepage

Course has several components:Lecture: (me talking, demos and Active learning)Discussion sections (group problem solving)Homework sets, Web basedLabs: (group exploration of physical phenomena)If you miss a lab or discussion you should always try to make it up as

soon as possible in another section!!

The first few weeks of the course should be review, hence the pace is fast. It is important for you to keep up!

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Physics 111: Lecture 1, Pg 3

Lecture OrganizationLecture Organization Three main components:Three main components:

Lecturer discusses class material

» Follows lecture notes very closely

Lecturer does as many demos as possible

» If you see it, you gotta believe it!

» Look for the symbol

Students work in groups on conceptual“Active Learning” problems

» Usually three per lecture

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Physics 111: Lecture 1, Pg 4

Scope of Physics 111Scope of Physics 111

Classical Mechanics:Classical Mechanics:

Mechanics: Mechanics: How and why things workClassical: Classical:

» Not too fast (v << c)

» Not too small (d >> atom)

Most everyday situations can be described in these terms.Most everyday situations can be described in these terms.Path of baseballOrbit of planetsetc...

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Physics 111: Lecture 1, Pg 5

How we measure things! All things in classical mechanics can be expressed in terms

of the fundamental units:fundamental units:

Length LMass MTime T

For example:Speed has units of L / T (i.e. miles per hour).Force has units of ML / T2 etc... (as you will learn).

UnitsUnits

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Physics 111: Lecture 1, Pg 6

Length:Length:

DistanceDistance Length (m)Length (m)

Radius of visible universe 1 x 1026

To Andromeda Galaxy 2 x 1022

To nearest star 4 x 1016

Earth to Sun 1.5 x 1011

Radius of Earth 6.4 x 106

Sears Tower 4.5 x 102

Football field 1.0 x 102

Tall person 2 x 100

Thickness of paper 1 x 10-4

Wavelength of blue light 4 x 10-7

Diameter of hydrogen atom 1 x 10-10

Diameter of proton 1 x 10-15

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Physics 111: Lecture 1, Pg 7

Time:Time:

IntervalInterval Time (s)Time (s)

Age of universe 5 x 1017

Age of Grand Canyon 3 x 1014

32 years 1 x 109

One year 3.2 x 107

One hour 3.6 x 103

Light travel from Earth to Moon 1.3 x 100

One cycle of guitar A string 2 x 10-3

One cycle of FM radio wave 6 x 10-8

Lifetime of neutral pi meson 1 x 10-16

Lifetime of top quark 4 x 10-25

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Physics 111: Lecture 1, Pg 8

Mass:Mass:

ObjectObject Mass (kg)Mass (kg)

Milky Way Galaxy 4 x 1041

Sun 2 x 1030

Earth 6 x 1024

Boeing 747 4 x 105

Car 1 x 103

Student 7 x 101

Dust particle 1 x 10-9

Top quark 3 x 10-25

Proton 2 x 10-27

Electron 9 x 10-31

Neutrino 1 x 10-38

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Physics 111: Lecture 1, Pg 9

Units...Units...

SI (Système International) Units:SI (Système International) Units:mks: L = meters (m), M = kilograms (kg), T = seconds (s)cgs: L = centimeters (cm), M = grams (gm), T = seconds (s)

British Units:British Units:Inches, feet, miles, pounds, slugs...

We will use mostly SI units, but you may run across some problems using British units. You should know how to convert back & forth.

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Physics 111: Lecture 1, Pg 10

Converting between different systems of unitsConverting between different systems of units

Useful Conversion factors:1 inch = 2.54 cm1 m = 3.28 ft1 mile = 5280 ft 1 mile = 1.61 km

Example: convert miles per hour to meters per second:

s

m4470

s

hr

3600

1

ft

m

283

1

mi

ft5280

hr

mi1

hr

mi 1 .

.

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Physics 111: Lecture 1, Pg 11

This is a very important tool to check your workIt’s also very easy!

Example:Example:

Doing a problem you get the answer distance

d = vt 2 (velocity x time2)

Units on left side = L

Units on right side = L / T x T2 = L x T

Left units and right units don’t match, so answer must be Left units and right units don’t match, so answer must be wrong!!wrong!!

Dimensional Analysis Dimensional Analysis

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Physics 111: Lecture 1, Pg 12

Lecture 1, Lecture 1, Act 1Act 1Dimensional AnalysisDimensional Analysis

The periodThe period PP of a swinging pendulum depends only on of a swinging pendulum depends only on the length of the pendulumthe length of the pendulum dd and the acceleration of and the acceleration of gravitygravity gg..Which of the following formulas forWhich of the following formulas for PP couldcould be be

correct ?correct ?

Pdg

2Pdg

2(a)(a) (b)(b) (c)(c)

Given: d has units of length (L) and g has units of (L / T 2).

P = 2 (dg)2

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Physics 111: Lecture 1, Pg 13

Lecture 1, Lecture 1, Act 1Act 1 SolutionSolution

Realize that the left hand side P has units of time (TT ) Try the first equation

P dg2 2(a)(a) (b)(b) (c)(c)

(a)(a) LL

T

L

TT

2

2 4

4 Not Right !!Not Right !!

Pdg

2Pdg

2

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Physics 111: Lecture 1, Pg 14

LL

T

T T

2

2

P dg2 2(a)(a) (b)(b) (c)(c)

(b)(b) Not Right !!Not Right !!

Try the second equation

Lecture 1, Lecture 1, Act 1Act 1 SolutionSolution

Pdg

2Pdg

2

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Physics 111: Lecture 1, Pg 15

TT

TLL 2

2

P dg2 2(a)(a) (b)(b) (c)(c)

(c)(c) This has the correct units!!This has the correct units!!

This must be the answer!!This must be the answer!!

Try the third equation

Lecture 1, Lecture 1, Act 1Act 1 SolutionSolution

Pdg

2Pdg

2

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Physics 111: Lecture 1, Pg 16

Motion in 1 dimensionMotion in 1 dimension In 1-D, we usually write position as x(t1 ).

Since it’s in 1-D, all we need to indicate direction is + or .

Displacement in a time t = t2 - t1 is x = x(t2) - x(t1) = x2 - x1

t

x

t1 t2

x

t

x1

x2some particle’s trajectory

in 1-D

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Physics 111: Lecture 1, Pg 17

1-D kinematics1-D kinematics

tx

tt)t(x)t(x

v12

12av

t

x

t1 t2

x

x1

x2trajectory

Velocity v is the “rate of change of position” Average velocity vav in the time t = t2 - t1 is:

t

Vav = slope of line connecting x1 and x2.

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Physics 111: Lecture 1, Pg 18

Consider limit t1 t2

Instantaneous velocity v is defined as:

1-D kinematics...1-D kinematics...

dt)t(dx

)t(v

t

x

t1 t2

x

x1

x2

t

so v(t2) = slope of line tangent to path at t2.

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Physics 111: Lecture 1, Pg 19

1-D kinematics...1-D kinematics...

tv

tt)t(v)t(v

a12

12av

Acceleration a is the “rate of change of velocity” Average acceleration aav in the time t = t2 - t1 is:

And instantaneous acceleration a is defined as:

2

2

dt)t(xd

dt)t(dv

)t(a

dt)t(dx

)t(v using

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Physics 111: Lecture 1, Pg 20

RecapRecap

If the position x is known as a function of time, then we can find both velocity v and acceleration a as a function of time!

adv

dt

d x

dt

2

2

vdx

dt

x x t ( )

x

a

vt

t

t

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Physics 111: Lecture 1, Pg 21

More 1-D kinematicsMore 1-D kinematics

We saw that v = dx / dt In “calculus” language we would write dx = v dt, which we

can integrate to obtain:

2

1

t

t12 dttvtxtx )()()(

Graphically, this is adding up lots of small rectangles:

v(t)

t

+ +...+

= displacement

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Physics 111: Lecture 1, Pg 22

High-school calculus:

Also recall that

Since a is constant, we can integrate this using the above rule to find:

Similarly, since we can integrate again to get:

1-D Motion with constant acceleration1-D Motion with constant acceleration

constt1n

1dtt 1nn

adv

dt

vdx

dt

0vatdtadtav

002

0 xtvat21

dt)vat(dtvx

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Physics 111: Lecture 1, Pg 23

RecapRecap So for constant acceleration we find:

atvv 0

200 at

2

1tvxx

a const

x

a

v t

t

t

Planew/ lights

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Physics 111: Lecture 1, Pg 24

Lecture 1, Lecture 1, Act 2Act 2Motion in One DimensionMotion in One Dimension

When throwing a ball straight up, which of the following is When throwing a ball straight up, which of the following is true about its velocity true about its velocity vv and its acceleration and its acceleration aa at the at the highest point in its path?highest point in its path?

(a)(a) BothBoth v = 0v = 0 andand a = 0a = 0..

(b)(b) v v 0 0, but , but a = 0a = 0..

(c) (c) v = 0v = 0, but , but a a 0 0..

y

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Physics 111: Lecture 1, Pg 25

Lecture 1, Lecture 1, Act 2Act 2Solution Solution

x

a

vt

t

t

Going up the ball has positive velocity, while coming down Going up the ball has positive velocity, while coming down it has negative velocity. At the top the velocity is it has negative velocity. At the top the velocity is momentarily zero.momentarily zero.

Since the velocity is Since the velocity is

continually changing there mustcontinually changing there must

be some acceleration.be some acceleration. In fact the acceleration is caused In fact the acceleration is caused

by gravity ( by gravity (g = 9.81 g = 9.81 m/sm/s22).). (more on gravity in a few lectures)(more on gravity in a few lectures)

The answer is (c) The answer is (c) v = 0v = 0, but , but a a 0 0. .

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Physics 111: Lecture 1, Pg 26

Derivation:Derivation:

Plugging in for t:

atvv 0 200 at

21

tvxx

Solving for t:

avv

t 0

200

00 avv

a21

avv

vxx

)xx(a2vv 02

02

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Physics 111: Lecture 1, Pg 27

Average VelocityAverage Velocity

Remember that atvv 0

v

t

t

v

vav

v0

vv2

1v 0av

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Physics 111: Lecture 1, Pg 28

Recap:Recap: For constant acceleration:

atvv 0

200 at

2

1tvxx

a const

From which we know:

v)(v21

v

)x2a(xvv

0av

02

02

Washers

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Physics 111: Lecture 1, Pg 29

Problem 1Problem 1

A car is traveling with an initial velocity v0. At t = 0, the driver puts on the brakes, which slows the car at a rate of ab

x = 0, t = 0ab

vo

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Physics 111: Lecture 1, Pg 30

Problem 1...Problem 1...

A car is traveling with an initial velocity v0. At t = 0, the driver puts on the brakes, which slows the car at a rate of ab. At what time tf does the car stop, and how much farther xf does it travel?

x = xf , t = tf

v = 0

x = 0, t = 0ab

v0

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Physics 111: Lecture 1, Pg 31

Problem 1...Problem 1...

Above, we derived: v = v0 + at

Realize that a = -ab

Also realizing that v = 0 at t = tf :

find 0 = v0 - ab tf or

tf = v0 /ab

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Physics 111: Lecture 1, Pg 32

Problem 1...Problem 1...

To find stopping distance we use:

In this case v = vf = 0, x0 = 0 and x = xf

fb2

0 x)a(2v

b

20

f a2v

x

)x2a(xvv 02

02

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Physics 111: Lecture 1, Pg 33

Problem 1...Problem 1...

So we found that

Suppose that vo = 65 mi/hr = 29 m/s Suppose also that ab = g = 9.81 m/s2

Find that tf = 3 s and xf = 43 m

b

20

fb

0f a

v

2

1x ,

a

vt

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Physics 111: Lecture 1, Pg 34

Tips:Tips:

Read !Before you start work on a problem, read the problem

statement thoroughly. Make sure you understand what information is given, what is asked for, and the meaning of all the terms used in stating the problem.

Watch your units !Always check the units of your answer, and carry the units

along with your numbers during the calculation.

Understand the limits !Many equations we use are special cases of more general

laws. Understanding how they are derived will help you recognize their limitations (for example, constant acceleration).

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Physics 111: Lecture 1, Pg 35

Recap of today’s lectureRecap of today’s lecture Scope of this courseScope of this course Measurement and Units Measurement and Units (Chapter 1)(Chapter 1)

Systems of units (Text: 1-1)Converting between systems of units (Text: 1-2)Dimensional Analysis (Text: 1-3)

1-D Kinematics 1-D Kinematics (Chapter 2)Average & instantaneous velocity

and acceleration (Text: 2-1, 2-2)Motion with constant acceleration (Text: 2-3)

Example car problemExample car problem (Ex. 2-7)(Ex. 2-7)

Look at Text problems Chapter 2: # 6, 12, 56, 119 Chapter 2: # 6, 12, 56, 119