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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*uilibriu&irst Con"ition of E*uilibriu&
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*uilibriu&irst Con"ition of E*uilibriu&
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&
irst Con"ition of E*uilibriu&
E+!&(le,
601 =θ
FLFLy
FLx
L+ 5 lLl cos
=sin of !n$le>
'he $reen
"!she" lines!re y
co&(onents.
'he yello#
"!she" lines
!re +co&(onents.
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E*uilibriu&
irst Con"ition of E*uilibriu&
E+!&(le,
FLFLy
FLx
?olution for FLx @L+ 5 -=67.68>=cos A:>
L+ 5 -72.77
?olution for FLy @Ly 5 =67.68>=sin A:>
Ly 5 8.D:
θ1 = 60°
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E*uilibriu&
irst Con"ition of E*uilibriu&
E+!&(le,
FRFRy
FRx
R+ 5 lRl cos
=sin of !n$le>
θ2
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E*uilibriu&
irst Con"ition of 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&
irst Con"ition of 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 $r!ity 5 9.6&/s2
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E*uilibriu&
irst Con"ition of E*uilibriu&
E+!&(le,
W
?olution for 4+ @
4+5 =96.::>=cos 28:o>
4+ 5 :
?olution for 4 y @
4 y 5 =96.::>=sin 28:o>
4 y 5 -96.::
4 5 =1:.:: ;$>=9.6: &/s2>
4 5 96.::;$&/s2 or 96.::
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E*uilibriu&
?u&&!tion of co&(onents
of the ectors
FRxFLx
F F : 5 G+
lLl cos
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E*uilibriu&
?u&&!tion of co&(onents
of the ectors
FRxFLx
F F : 5 :
lLl cos =-72.77>
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E*uilibriu&
?u&&!tion of co&(onents
of the ectors
F F 5 G y
lLl sin
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E*uilibriu&
?u&&!tion of co&(onents
of the ectors
F F 5 :
lLl sin
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E*uilibriu&
?u&&!tion of Concurrent orces
5 G
5 'ot!lorce
G+ F G y
?u&&!tion of+ co&(onent
?u&&!tion of y co&(onent
F
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E*uilibriu&
?u&&!tion of Concurrent orces
5 :
5 'ot!lorce
:
?u&&!tion of+ co&(onent
?u&&!tion of y co&(onent
F
:F
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E*uilibriu&
'hree 'y(es of E*uilibriu&
1. ?t!ble E*uilibriu&
- occurs #hen !n ob0ect is (l!ce" in such
! f!shion th!t !n effort to "isturb it#oul" re*uire its CH to be r!ise".
E+!&(le, ! boo; lyin$ 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 ?us(ension/
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 ?us(ension/
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