Chapter 2 Fundametal of Physics Dong Luc Hoc Pham Hong Quang

8/16/2019 Chapter 2 Fundametal of Physics Dong Luc Hoc Pham Hong Quang

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Fundamental of Physics

PETROVIETNAM UNIVERSITY

FUNDAMENTAL SCIENCE DEPARTMENT

Hanoi, August 2012

Pham Hong QuangE-mail: [email protected]



2

Pham Hong Quang 2 Fundamental

Chapter 2

The Laws of Motion

2.1 The Concept of Force

2.2 Newton’s First Law and Inertial

Frames2.3 Newton’s Second Law

2.4 Newton’s Third Law

2. Some !pplications of Newton’s Laws2." Forces of Friction

2.# Moment$m and Imp$lse




%ham &on' ($an' Fundamental Science Department 3

Force

Forces are what cause any

change in the velocity of anobject

Newton’s denition:

A force is that which

causes an acceleration





•Contact forces involve

physical contact

between two objects

Ea!ples a" b" c

•Field forces act through

e!pty space

No physical contact

is re#uired

Ea!ples d" e" f





F$ndamental Forces

•$ravitational force

%etween objects

•Electro!agnetic forces

%etween electric charges

•Nuclear force

%etween subato!ic particles

•&ea' forces

Arise in certain radioactive decay

processes

•Note: (hese are all eld forces





)ector Nat$re of

Forces

(he forces are applied

perpendicularly to each

other

(he resultant )or net* force

is the hypotenuseForces are vectors" so you

!ust use the rules for

vector addition to nd the

22 ’ d l



2.2 Newton’s Frst Law and Inertal Frames


•“I an o!"ect doe# not interact $ith other o!"ect#% it

i# po##i!le to identi& a reerence rame in $hich the

o!"ect ha# 'ero acceleration(

(his is also called the la$ o inertia

+t denes a special set of reference fra!es called

inertial rame#

&e call this an inertial frame of reference

Any reference fra!e that !oves with constant

velocity relative to an inertial fra!e is itself an

inertial fra!e



2.2 Newton’s First Law and Inertial Frames


Newton’s First Law * !lternati+e

Statement•+n the absence of eternal forces" when viewed

fro! an inertial reference fra!e" an object at rest

re!ains at rest and an object in !otion continues

in !otion with a constant velocity

Newton’s First ,aw describes what happens in

the absence of a force

Also tells us that when no force acts on an

object" the acceleration of the object is -ero





!,o$t Mass

•Mass is that property of an object that species

how !uch resistance an object ehibits to

changes in its velocity

•.ass is an inherent property of an object

•.ass is independent of the object’s

surroundings

•.ass is independent of the !ethod used to

!easure it

•.ass is a scalar #uantity

•





Mass +s. -ei'ht.ass and weight are two di0erent

#uantities

&eight is e#ual to the !agnitude of thegravitational force eerted on the

object

&eight will vary with location

Ea!ple:

wearth 1 34 lb5 w!oon 6 74 lb

!earth 1 2 'g5 !!oon 1 2 'g



2.3 Newton’s Second Law


“)hen vie$ed rom an inertial reerence rame% the

acceleration o an o!"ect i# directl& proportional to

the net orce acting on it and inver#el& proportional

to it# ma##(

Force is the cause of change in !otion" as

!easured by the acceleration

Algebraically"

mmµ → =

∑∑

Fa F a

rr r





nit of Force

(he /+ unit of force is the newton )N*

N 1 'g8! 9 s2

(he / Custo!ary unit of force is a

po$nd )lb*

lb 1 slug8ft 9 s2

N 6 ; lb





/ra+itational Mass +s. Inertial Mass

+n Newton’s ,aws" the !ass is the inertial

!ass and !easures the resistance to a

change in the object’s !otion

+n the gravitational force" the !ass !easures

the gravitational attraction between the object

and the Earth

Eperi!ents show that gravitational !ass and

inertial !ass have the sa!e value



2.4 Newton’s Third Law


“I t$o o!"ect# interact% the orce e*erted !&

o!"ect + on o!"ect , i# equal in magnitude and

oppo#ite in direction to the orce e*erted !&

o!"ect , on o!"ect +

•Forces always occur in pairs

•A single isolated force cannot eist

• (he action force is e#ual in

!agnitude to the reaction force and

opposite in direction

12 21= −F F

r r

12 F

21 F


http://slidepdf.com/reader/full/chapter-2-fundametal-of-physics-dong-luc-hoc-pham-hong-quang 15/38%ham &on' ($an' Fundamental Science Department 15

!ction0eaction

• (he nor!al force )tableon !onitor* is thereaction of the force the!onitor eerts on thetable

Nor!al !eansperpendicular" in thiscase

•

(he action )Earth on!onitor* force is e#ualin !agnitude andopposite in direction tothe reaction force" the

force the !onitor eerts



2.5 Some Applications of Newton’s Laws


Free od ia'ram

(he !ost i!portant step in solvingproble!s involving Newton’s ,aws

is to draw the free body diagra!:

+n a free body diagra!" you want

the forces acting on a particularobject

%e sure to include only the forces

acting on the object of interest

+nclude any eld forces acting on

the object

can neglect reaction forces

25SomeApplcatonsofNe ton’sLa s



2.5 Some Applcatons of Newton’s Laws


+nitially dealing with frictionless surfaces.asses of strings or ropes are negligible

(he force the rope eerts is away fro! the object

and parallel to the rope&hen a rope attached to an object is pulling it"

the !agnitude of that force is the tension in the

rope





%articles in 56$ili,ri$m

• +f the acceleration of an object that can be

!odeled as a particle is -ero" the object is said to

be in e6$ili,ri$m

(he !odel is the particle in equili!rium model

• .athe!atically" the net force acting on the

object is -ero 0

0 and 0

=

= =

∑

∑ ∑ x y F F

F





! lamp s$spended

A la!p is suspendedfro! a chain of negligible

!ass

(he forces acting on the

la!p are

the downward force of

gravity

the upward tension in the

chain

Applying e#uilibriu!

0 0= → − = → =∑ y g g F T F T F





Find the tension in the three

ca,les

)a* A tra<c light weighing 2= N suspended by cables>)b* Free?body diagra! for the tra<c light> )c* Free?body

diagra! for the 'not where the three cables are joined>









%articles nder a Net Force

•+f an object that can be !odeled as a

particle eperiences an acceleration" there

!ust be a non-ero net force acting on it.odel is particle under a net orce

model

•

@raw a free?body diagra!•Apply Newton’s /econd ,aw in co!ponent

for!





Newton’s Second

Law7

•Forces acting on the

crate:

A tension" acting

through the rope" is the

!agnitude of force

(he gravitational force"

(he nor!al force" "

eerted by the oor





Newton’s Second Law7 cont.

•Apply Newton’s /econd ,aw in co!ponent for!:

•/olve for the un'nown)s*

•+f the tension is constant" then a is constant and

the 'ine!atic e#uations can be used to !ore

fully describe the !otion of the crate

x x F T ma= =∑

0y g g F n F n F = − = → =∑





!twood’s

machineAn Atwood’s !achine is two !asses connected

by a strong light string that are hung over an

ideal pulley )light and frictionless*>

(he !asses have identical velocity and

acceleration !agnitudes at every instant>

+f we dene up on the left and down on the right

as positive directions" then the !asses have

identical velocities and accelerations period>





!twood’s machine7

cont.

)( 21

,

mm

F a

cwnet

cw +=

)( 21

12

mm

g m g macw +

−=

2

21 t ah cw=





Note !,o$t the

Normal Force

(he nor!al force is not

always e#ual to the

gravitational force of the

object

For ea!ple" in this case

!ay also be less than

0

and

y g

g

F n F F

n F F

= − − =

= +

∑

n F

g

i i





Inclined %lanes

•Forces acting on the object:

(he nor!al force acts

perpendicular to the plane

(he gravitational force acts

straight down

•Choose the coordinate syste!

with * along the incline and &

perpendicular to the incline

•Beplace the force of gravity

with its co!ponents

5 li i f





M$ltiple 8,9ects7

Concept$ali:e•&hen two or !ore

objects are connected

or in contact" Newton’s

laws !ay be applied to

the syste! as a whole

and9or to each

individual object

•&hichever you use to

solve the proble!" the

other approach can be

used as a chec'

5 li i f





%ro,lem0Sol+in' &ints Newton’s Laws

•

onceptuali'e @raw a diagra!

Choose a convenient coordinate syste! for each

object

•ategori'e

+s the !odel a particle in e#uilibriu!

+f so" ΣF 1 4

+s the !odel a particle under a net force

+f so" ΣF 1 m a

25S A li i fN ’L





%ro,lem0Sol+in' &ints Newton’s Laws7

cont•Analy-e

@raw free?body diagra!s for each object

+nclude only forces acting on the object

Find co!ponents along the coordinate aes%e sure units are consistent

Apply the appropriate e#uation)s* in co!ponent

for!

/olve for the un'nown)s*

•Finali-e

Chec' your results for consistency with your free?

body diagra!

26F fFiti



2.6 Forces of Friction


•&hen an object is in !otion on a surface

or through a viscous !ediu!" there will

be a resistance to the !otion

(his is due to the interactions

between the object and its

environ!ent

• (his resistance is called the orce o

riction

26F fFiti





Friction isproportional tothe normal force

# ≤ /s n and 0 1 /0 n

D is the

coe;cient of

friction

•

(hese e#uationsrelate the

!agnitudes of the

forces" they are not

26F fFiti





• (he coe<cient of friction depends on the

surfaces in contact

• (he force of static friction is generally

greater than the force of 'inetic friction

• (he direction of the frictional force is

opposite the direction of !otion and

parallel to the surfaces in contact

• (he coe<cients of friction are nearly

independent of the area of contact

26F fFiti





Friction in Newton’s ,aws roble!s

•Friction is a force" so it si!ply is included

in the in Newton’s ,aws

• (he rules of friction allow you to

deter!ine the direction and !agnitude of

the force of friction

27M t dI l



2.7 Momentum and Impulse


Newton’s /econd ,aw can read

.o!entu! 1 !ass × velocity:

@erivative of the !o!entu! of anobject with respect to the ti!e

interval during which the objectchanges its velocity e#uals the netforce acting on the objectG

am F =

dt

vmd

dt

vd m F

)(==

vm p =

27M t dI l



2.7 Momentum and Impulse


+ntegral fro! t to t2 we get:

(he change of !o!entu! of an object

during the ti!e fro! t to t2 e#uals the

i!pulse acting on it during that ti!eG

dt F pd .=

pulsedt F p p p Im.

2

1

12 ≡=−=∆ ∫



Thank you!

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Chapter 2 Fundametal of Physics Dong Luc Hoc Pham Hong Quang