fundamental physics - force & motion (print)

7/24/2019 Fundamental Physics - Force & Motion (Print)

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Fundamental Physics I

Force and Motion

Sutarto

University of Indonesia

2014


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Cross Product

FB= qv !B

Simbol operasi Cross

Cross:Perintah untuk mencari komponen

vyang TEGAK LURUS B

Dot Product

W= F!s

Simbol operasi Dot

Dot:Perintah untuk mencari

komponen Fyang SEJAJAR s

z(k)

y(j)

x(i)

z(k)

y(j)

x(i)

i x i = 0j x j = 0k x k = 0

i !i = 1j !j = 1k !k = 1

i x j = +ki x k = -j

j x k = +ij x i = -k

k x i = +jk x j = -i

i !j = 0, j !k = 0, k !i = 0i !k = 0, j !i = 0, k !j = 0


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!ahulu Kala

Aristoteles" A moving object needs a force to keep it moving

Galileo" An object at rest will stay at rest, unless a force cause it to start

moving" A moving object will continue to move at a steady speed in a

straight line, unless a force acts on it


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!ahulu Kala

Steady speed in a straight line: constant velocity

The conclusion:Uniform motion is the natural state of motion of an object. Here,uniform means moving with constant velocity or steady speed in astraight line

Sir Isaac Newton, The First Law

" An object will remain at restor in a state of uniform motionunless it is acted on by a net external force

This statement, in fact, already contained the simple (but cool) equation:F= ma

No force, no acceleration. No change in the path of motion and itsspeed.


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#$echnica%y&!eeper

Kasus 1:

Bola golf dipukul secara mendatar. Untuk sementarakita abaikangesekan bola dengan lintasan maupundengan udara di sekitarnya.

Mula-mula diam (kecepatan = 0). Setelah

dipukul, bergerak (mempunyaikecepatan)

Pemukul memberikan gaya(dorongan) ke bola. TerjadiKONTAK antara pemukul

dan bola.

Akibatnya, bola bergerak searahdengan arah kerja gaya. Padagambar di atas, arah tersebutditunjukkan oleh panah to hole1. Kapan (berapa lama) bola golf

mengalami percepatan? 2. Setelah dipukul, bola golf bergerak

dengan (a) kecepatan konstan, (b)

percepatan konstan


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'ormulasi Gerak Lurus

Jadi, bola golf mengalami percepatan hanyasaat terjadi kontak antara pemukul dan bola.Dengan kata lain, percepatan dialami selamagaya bekerja.

Setelah kontak antara pemukul dan bolausai, maka bola akan bergerak tanpapercepatan"dengan kecepatan tetap.

Kecepatan tetap berarti perpindahan yang dialami oleh bola tiap detik (Generally,tiap satu satuan waktu) juga tetap.


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'ormulasi Gerak LurusKetika bendabergerak, bendamengalamiperubahan posisi.

Perubahan posisidisebutperpindahan.

Untuk menentukan

perpindahan, kitaharus menentukanposisi bendaterlebih dahulu,yaitu posisi awaldan posisi akhir.

Question

Mana yang lebihdahulu ada, lintasanatau gerak benda?


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VektorThis is a Cartesian axis.Position specified by twocoordinate numbers.

This is a point c. It consists oftwo coordinate, namely xandy

and written as c (x, y) = c (3, -3).

Horizontal axis (called x)IND: Absis

Vertical axis (calledy)IND: Ordinat

In 2D system:

Position (and othervector quantities) can be

characterized by twomethods:# Points

# Segments

We called it VECTOR.

There are only Additionand Multiplication of

vectors.


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Components of Vectors

Components of Vectors:Vector Ahas two components

(number of components also tell us about

the dimension of the vectors)

#

X Component:Ax= Acos !

#

Y Component:

Ay= Asin !

Finding the components of a vectoris a process of projectingthe vector

to the coordinate axis.

The component of Aalong EF is B.

Vektor


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Vectors in 3D

Vector R has three components,i.e. R1, R2, and R3.

Vector 3D notations:R = x1i+y1j+ z1k

C

omponentsofvector

Component

sofvector

Vektor


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Equa(on of Mo(on

Jika benda bergerak pada lintasan lurus, maka besarnyaperpindahansama dengan panjang lintasanyang ditempuh benda. Panjang lintasandisebut jarak.

Case 1:

Benda bergerak dengan kecepatan konstan (artinya kelajuan dan

arahnya tetap)

Peprindahan (t) = Posisi awal (t = 0) + Kecepatan x Waktu

x (t) = x0+ vt


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No force, no acceleration. No change

in the path of motion and its speed


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What if the NetForce is not zero?

!F #0

Always remember:1. Rest"Move or Move "Rest2. Change in velocity


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The results is:

# The rest object will moves

The net forces

gives

acceleration

to the

object#

The velocity of the moving object will

change

The net forcesgivesaccelerationto the

object


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Acceleration

Acceleration is defined asthe rate of changeof velocity with respect to time.

Constant Acceleration (Constant Force) # It can increases or decreases the velocity. # It can changes the direction of the objects motion.

Nonconstant Acceleration (Non Constant Force)# It can increases or decreases the velocity. # It can changes the direction of the objects motion.

1

2

This part is notour business!

intervalTime

velocityofchangeofrateTheonAccelerati =

a

!

vvv

!!!

!="initfinal

ttt !="initfinal

(m/s)/s"m/s2


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'ormulasi Gerak LurusKetika bendabergerak, bendamengalamiperubahan posisi.

Perubahan posisidisebutperpindahan.

Untuk menentukan

perpindahan, kitaharus menentukanposisi bendaterlebih dahulu,yaitu posisi awaldan posisi akhir.

Question!Mana yang lebihdahulu ada, lintasanatau gerak benda?


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t1

t2

t3

Equa(on of Mo(on

Agar bendamengalamipercepatan makaharus ada gayayang bekerja secaraterus menerus pada

benda

Anggaplahterdapat sebuahbenda yangdidorong dengan

gaya konstan (besardan arahnya tetap),maka benda akanmengalamiperpindahan.


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Acceleration and InstantaneousAcceleration

[ ]2-2

initfinal

LTm/s

sandm/s

Time

changeVelocity

!=

="="

"

"=

"

#=

=

a

tv

t

v

t

vv

a

!

!

!!!

!

1 Average Acceleration

dt

vd

t

v

t

vva

t

t

!!

!!

!

=

!

!=

!

"=

#!

#!

0

initfinal

0

lim

lim

2 Instantaneous Acceleration

Graph of Velocity Time

2

2

dt

xda

dt

xdv

dt

vda

!

!

!

!

!

!

=

=!=

t

va

!

!=

!

!

Equa(on of Mo(on


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"t

InstantaneousVelocity

( )( )

( ) ( )

dt

xdv

t

xv

t

txttxv

ttt

txx

ttxx

t

xxv

t

t

t

t

!

!

!

!

!!

!

!!

!!

!!

!

=

!

!=

!

"!+=

"=!

=

!+=

!

"=

#!

#!

#!

#!

inst

0inst

0inst

12

1

2

12

0inst

lim

lim

:where

lim

0

"x

Equa(on of Mo(on


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1 Uniform and Non-uniform Motion

2 Constant Speed

3 Constant Acceleration

Constant speed

Constant Acc

xvs t

vvs t

Distance (t) = initial position (t = 0) + velocity x time

x (t) = x0+ vt

Distance (t) =

initial position (t = 0) +velocity (average) x time

x(t) = x0+ vaveraget



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# Terminology

1. Motion

2.

Position

3. Displacement

4. Distance

5. Velocity (Average and Instantaneous Velocity)

6. Speed (Average and Instantaneous Speed)

7.

Time (and Time Interval)

12(x1, x2,)

4 3

t1 t2

7

MathTalk!



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[ ]1-LTm/s

secondandmeter

Time

ntDisplaceme

!=

="="!"

"=

=

v

tx

t

x

v

!

!

!

!

1 Velocity (and Average Velocity)

[ ]1-LTm/s

Time

distanceTotal

!=!"

=

=

#v

t

x

v

2 Speed (and Average Speed)

t

xv

!

!=

!

!

t

x

v

!=

"

vvxx !!!!

and

Look!



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3 InstantaneousVelocity

dt

xdv

!

!

=inst

4 InstantaneousSpeed

dt

dxv =inst

For this case:

vv

dt

dx

dt

xddxxd

=

=!=

inst

!

!

!

3

4Constant rate of change of position gives

constant or uniform velocity (or speed)



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Mathematical Formulation

1. Initial Position, x02. Initial Velocity, v0

# Motion with constant speed (GLB)

x(t) = x0+ vt

# Motion with constant Acceleration (GLBB)x(t) = x0+ vaveraget

Acceleration = avaverage= $(v0+ v)v= (v0 + at) vaverage= v0t+ $at

2

x(t) = x0

+ v0

t+ $at2



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Briefsummary

1Motion with constant speed/velocity (GLB)

# Quantities$

Length (distance or displacement)$ Time$

Velocity/Speed

#

Formulax= x0+ vt"x0= 0, x= vt

2 Motion with constant acceleration (GLBB) # Quantities

$

Length (distance or displacement)$ Time$

Velocity/Speed$

Acceleration

# Formula

x(t) = x0+ v0t+ $at2

# Other Useful Formula: $ v(t) = v0 at$ v2= v0

2 2a%x$ x (t) = x0+ vaveraget

E

xample

(Quiz 1):An amateur bowler releases aball with initial velocity 3.0 m/s;the ball slow down with aconstant acceleration 0.2 m/s2.

a. How far does the ball rollbefore stopping and howlong does it takes to stop?

b. How long it takes to reducesits velocity to 1.0 m/s?

c.

Draw the position timegraph, velocity time graphand acceleration timegraph.



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Free Falling Objects: The Art of Gravity


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Free Falling Objects: The Art of Gravity

Attraction


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Earth has its own natural

acceleration (called Gravity)

that attract any object.

And, the object will moves

toward the earth surface with

constant acceleration.

An Object is placed abovethe earth surface (H)



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# Free falling objects:

$ Freemeans there is noinitial velocity or v0= 0.

$ Fallingmeans the objectsalways move toward theearth surface.

$ Objectsmeans everyphysical quantity includinglight.

# Is it kinds of Straight LineMotion?

# Mathematical Formulation: Gravity (g) =Acceleration (a)

$

Objects move straight up= Deceleration.$ Objects move straight

down = Acceleration.

h(t) = h0+ v0t $gt2


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E

xample (Quiz 2):A ball is thrown straight upwith a speedof10.0 m/s from a third-floor window thatlocated 15.0 m above the ground. Calculate:

a. The maximum height of the ball. b.

Total time for the ball to reach themaximum height.

c. The balls velocity when it hits the ground. d. Total time it takes to reach the ground. e. Total time it takes to drop from height 10.0

m to 5.0 m.

f. Draw the position time graph, velocity time graph and acceleration time graph

Use g= 10.0 m/s2.

Free FallingObjects



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Assumption:

# The trajectory is parabolic. # No friction. # The free-fall acceleration gis

constant over the range of motionand is directed downward.

cos= vx/ v0sin= vy/ v0

)f, *e net force is not zero


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Newtons Laws of

Motions

3.1Force

& Interactions

# Definition:Force is a pullor a pushthat acted on a

thing or body

# It is a vectorquantity, so:It has m gnitudeand dire tion

# Symbol: F

# Measured in Newton(SI system) and dyne(cgs system)

A pull

A push


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Kinds of Interactions:#

Contact

#

Non contact

Kinds of Forces:# Contact Forces#

Field Forces

Newtons Laws of

Motions

3.1Force

& Interactions


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3.2 Newtons 1st

Law:Inertia

It states that:

when there is no net forceacting on an object, the object maintainits initial condition (rest) or motion with

constantvelocity

In other words:

when an object moves with

constantvelocity, the net forceacting on it must be zero

Newtons Laws of

Motions


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1Net Force = 0

F = 0

We called it:

Equilibrium

2Rest or Constant Velocity

v= 0 v= constant

We (also) called it:

Equilibrium


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For the same object:

# The biggerthe net force, the fasterobject will moves

For the same net force:

# The bigger the massof the object, the slowerobject willmoves

F! "#$v

$t"% a"

m!" #v#t$% a$


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3.2 Newtons 2stLaw

We can start by saying:

an object acted upon a net forceaccelerates

Newtons Laws of

Motions


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Warning

ma is not a FORCE! All forces on an objects are added as a vector to generate thenet force on the left side of the above equation. ma then just aphysical result of the net force that acts on an object which has

mass m.

!

F! = m!

a


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Some Particular

Forces

1

The Gravitational Force

# Due to the gravitational accelerationof the Earth

# Acts on everything that has mass

# Type of pull force (never push)

Weight

Weight is the magnitude of the net forcerequired to prevent the body from falling freely

# Fnet= may"W Fg= m(0)

# So, W= Fg= mgj

i

k

!

F =mg !j( )!

F =m!

g"!

g = !gj


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2The Normal Force

Normalmeans

e

r

p

e

n

d

i

c

u

l

r

Surface

Surface

Surface

Surface

Normal Normal

Gravity

Not normal

Normal

Normal

Gravity Gravity cos

FN !Fg = may

FN = mg+ may " m g+ ay( )FN = mg" ay = 0


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FN= mgcosWhere= angle between normal and gravity

In almost all situation, we have

!


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!#$%&'%()

# Static Friction

Relative velocity = NO#

Kinetic Friction

Relative velocity = YES

! #$%&'( &)*( +, +--+(.*/ 0.1/)*.+, *+

*2/ +34/)* 5+6/5/,*7 1/$&*.6/$' !


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4Tension

8/ &((95/:

;)+5-&1/0 *+ *2/ +34/)* %2/1/ *2/ 1+-/ &**&)2/0?

@

fundamental physics - force & motion (print)

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