Equilibrium Powerpoint Physics 12 Lecture

8/9/2019 Equilibrium Powerpoint Physics 12 Lecture

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EQUILIBRIUM

M r . D

J o h n R

e b

C l e o f e

P h y s i c

s 1 2

L e c t u

r e


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DEFINITION OF EQUILIBRIUM

- ! con"ition in #hich !ll !ctin$influences !re c!ncelle" by others%

resultin$ in ! st!ble% b!l!nce"% orunch!n$in$ syste&.

- 'he st!te of ! bo"y or (hysic!l syste&!t rest or in un!cceler!te" &otion in

#hich the result!nt of !ll forces !ctin$on it is )ero !n" the su& of !ll tor*ues!bout !ny !+is is )ero.

E*uilibriu&


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E*uilibriu&

'#o Con"itions of E*uilibriu&,

1. o et orce

- the su&&!tion of forces !ctin$ on !

bo"y/ob0ect is e*u!l to )ero.

2. o et 'or*ue

- the su&&!tion of tor*ues !ctin$ on the

bo"y/ob0ect is e*u!l to )ero.

0=∑ F

0=∑

τ


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E*uilibriu&irst Con"ition of E*uilibriu&

or&ul!,

- the su&&!tion of the !n"

co&(onents shoul" be e*u!l to )ero.

in" the su&&!tion of !n" su&&!tion

of .

0=∑+∑=∑ X X

F F F

?=∑ X F

?=∑ Y F


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E*uilibriu&

irst Con"ition of E*uilibriu&

E+!&(le,

FL FR

W

3 bo+ is sus(en"e"

by t#o #ires. 'ell

#hether the bo+ is

in e*uilibriu& or not.

θ1 θ2

θ1

* θ2*

θ1 = *θ2 θ2 = *θ1


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E+!&(le,

FL FR

W'here !re there

!re three forces

(resent.

L% R !n" 4 !re

these forces.

θ1 θ2


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E+!&(le,

FL = 84.87 N FR = 49.00 N

W

L 5 67.68

R 5 79.::

4 5 1:.:: ;$

θ1 = 60°

θ1 = 60°

θ2 = 30°

θ2 = 30°


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E*uilibriu&


E+!&(le,

601 =θ

FLFLy

FLx

L+ 5 lLl cos

=sin of !n$le>

'he $reen

"!she" lines!re y

co&(onents.

'he yello#

"!she" lines

!re +co&(onents.


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E*uilibriu&


E+!&(le,

FLFLy

FLx

?olution for FLx @L+ 5 -=67.68>=cos A:>

L+ 5 -72.77

?olution for FLy @Ly 5 =67.68>=sin A:>

Ly 5 8.D:

θ1 = 60°


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E*uilibriu&


E+!&(le,

FRFRy

FRx

R+ 5 lRl cos

=sin of !n$le>

θ2


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E*uilibriu&


E+!&(le,

FRFRy

FRx

?olution for R+@R+ 5 =79.:>=cos :>

R+ 5 72.77

?olution for Ry@Ly 5 =79.:>=sin :>

Ly 5 27.D

θ2 = 30°


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E*uilibriu&


E+!&(le,

W

4+5 l4l cos θw

4+ 5 =&!$nitu"e of 4>

=cos of !n$le>

4 y 5 l4l sin θw

4 y 5 =&!$nitu"e of 4> =

sin of !n$le>

4 5 &!

& 5 &!ss 5 1:.: ;$

! 5 !cceler!tion "ue to $r!ity 5 9.6&/s2


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E*uilibriu&


E+!&(le,

W

?olution for 4+ @

4+5 =96.::>=cos 28:o>

4+ 5 :

?olution for 4 y @

4 y 5 =96.::>=sin 28:o>

4 y 5 -96.::

4 5 =1:.:: ;$>=9.6: &/s2>

4 5 96.::;$&/s2 or 96.::


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E*uilibriu&

?u&&!tion of co&(onents

of the ectors

FRxFLx

F F : 5 G+

lLl cos


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E*uilibriu&


of the ectors

FRxFLx

F F : 5 :

lLl cos =-72.77>


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E*uilibriu&


of the ectors

F F 5 G y

lLl sin


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E*uilibriu&


of the ectors

F F 5 :

lLl sin


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E*uilibriu&

?u&&!tion of Concurrent orces

5 G

5 'ot!lorce

G+ F G y

?u&&!tion of+ co&(onent

?u&&!tion of y co&(onent

F


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E*uilibriu&

?u&&!tion of Concurrent orces

5 :

5 'ot!lorce

:

?u&&!tion of+ co&(onent

?u&&!tion of y co&(onent

F

:F


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E*uilibriu&

'hree 'y(es of E*uilibriu&

1. ?t!ble E*uilibriu&

- occurs #hen !n ob0ect is (l!ce" in such

! f!shion th!t !n effort to "isturb it#oul" re*uire its CH to be r!ise".

E+!&(le, ! boo; lyin$ on ! t!ble

Point of ?us(ension/

Point of Cont!ct

'he re" "ot si$nifies

the center of$r!ity of the boo;.


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E*uilibriu&

2. Unst!ble E*uilibriu&

-! sli$ht "isturb!nce #ill "ro( the ob0ects

CH to ! lo#er (oint

-!n unst!ble ob0ects see;s st!bility byf!llin$ fro& ! s&!ller to ! l!r$er b!se of

su((ort. E+!&(le, ! stic; st!n"in$ on its

ertic!l (osition.


Point of Cont!ct

'he re" "ot si$nifiesthe center of

$r!ity of the stic;.


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E*uilibriu&

. eutr!l E*uilibriu&

-occurs #hen !n ob0ects CH is neither

r!ise" nor lo#ere" #hen it is "isturbe"

-re&!ins the s!&eE+!&(le, rollin$ b!ll

'he re" "ot si$nifies

the center of $r!ity

of the rollin$ b!ll.


Point of Cont!ct


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Homework:1.> 3 7.::9899:;$ cr!te is sus(en"e" by t#oro(es. 'he first ro(e h!s !n !n$le of 7Dfro& the hori)ont!l to the left !n" thesecon" ones !n$le is 8D fro& the ertic!l !tthe ri$ht. in" the tension in first ro(e if the' 2 5 7A.76.

2.> 3n ob0ect is h!n$in$ usin$ three strin$s th!th!s ! #ei$ht of 2D:.:::::::$. 'he firststrin$ is tie" to left !n" the other t#o !reconnecte" to ri$ht. 'he !n$le of the one on

the left is 1: fro& the hori)ont!l. 'he firststrin$ fro& the ri$ht is 1:: st!rtin$ fro&the left strin$ C4. 4hile the l!st strin$ is8 fro& the other one on the ri$ht si"e. 'heforce in the l!st strin$ is 17.A. in" !ll

the forces !n" erify if the syste& is ine*uilibriu&.

E*uilibriu&


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E*uilibriu&

En" ofPresent!tionJ

Equilibrium Powerpoint Physics 12 Lecture

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