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2.9 Equilibrium of Force
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Newton Memory
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find the resultant force
(c)
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(f)
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2.9 IDEA OF EQUII!"IUM FO"#E$
Newton 3rd Law of Motion : Action is e%ual to reaction
An object state that is in e%uili&rium when :
1. ………………………………………………………………………………………………
2. ………………………………………………………………………………………………
stationary object
An object movin with !niform ve"ocity
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#t is in a stationary state
#t is movin with !niform ve"ocity
Normal reaction, R Normal reaction, R
Weight, W=mg weight, W=mg
Magnitude of R = W Magnitude of R = mg cos θ
R and W acts in opposite direction. And acts in opposite direction.
So, Resultant force = W – R = 0 So ,Resultant force = mg cos θ – R =
0
( o!ect in e"uilirium # ( o!ect in e"uilirium #
normal reaction, R
friction force
force, $
Weight, W
$orce , $ = $rictional force
= –
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2.9.' Addition of Force
1. Addition of force is defined as ...……………………………………………………..
………………………………………………………………………………………………
………………………………………………………………………………………………
Examples : the forces are acting in one direction
$1 % 1& N
$2 % ' N
es!"tant force $
Example : the forces are acting in opposite directions
$1 % 1& N
$2 % ' N
es!"tant force $
Example : the forces are acting in different directions
$2 % ' N
'&& $
$1 % 1& N
*ara""e"oram method:1. +raw to sca"e.
2. +raw the "ine ,ara""e" with $1 to the ede of $2 and the "ine ,ara""e" with $2 to the ede of $1
3. -onnect the diaona" of the ,ara""e"oram startin from the initia" ,oint.
. Meas!re the "enth of the diaona" from the initia" ,oint as the va"!e of the res!"tant force.
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a res!"tant force is a sin"e force the
re,resents in manit!de and direction two or more forces actin on an object
$ res!"tant % the tota" of forces (inc"!din the directions of the forces)
= $ % & $ ' = %0 & = % N
= $ % ) $ ' = %0 ) = N
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$2
$
$1
/rian"e method
1. +raw to sca"e.
2. +is,"ace one of the forces to the ede of another force.
3. -om,"ete the trian"e and meas!re the res!"tant force from the initia" ,oint.
E(am)le '* +!rin 0,ort +ay two teams in t! of war com,etition ,!"" with forces of &&& N and
'3&& N res,ective"y. hat is the va"!e of the res!"tant force Are the two team in
e4!i"ibri!m
E(am)le 2* A boat in a river is ,!""ed hori5onta""y by two wor6men. or6men A
,!""s with a force of 2&& N whi"e wor6men whi"e wor6men 7 ,!""s with a force of 3&&
N. /he ro,es !sed ma6e an an"e 2'& with each other. +raw a ,ara""e"oram and "abe" the
res!"tant force !sin sca"e of 1 cm : '& N. +etermine the manit!de of res!"tant force.
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*/., $m
2,/
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2.9.2 "esolution of a force
1. eso"!tion of a force is …………………………………………………………………
θ
efer to trionometric form!"a:
E(am)le * /he fi!re be"ow shows A"i mo,,in the f"oor with a force '& N
at an an"e of && to the f"oor.
$ % '& N
E(am)le of reso"!tion and combination of forces
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re*erse process of +nding the resultant force
$ $ is the resultant force of $- and
$
herefore, $ can e resol*ed
into $- and $
$
/ertical $-
omponent
os θ =
F
F x
, therefore $ - = $ cos θ
Sin θ =
F
F y
, therefore $ = $ sin θ
$ -
$
mg = 100 N
600
F = ?
200 N
400
400
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+ro&lem sol,in-
1. hen a system is in e4!i"ibri!m ……………………………………………………….
2. #f a"" forces actin at one ,oint are reso"ved into hori5onta" and vertica"
com,onents ……………………………………………………………………………
3. 89am,"e 1 0how on a fi!re
a) the direction of tension force / of strin
b) the res!"tant force act to "am,
c) ca"c!"ate the manit!de of tension force /
m"am, % 1.' 6
"am, % 1.; N
E(ercise 2.9
1. /wo force with manit!de 1< N and N act a"on a straiht "ine. ith the aid of diarams determine
the ma9im!n ,ossib"e va"!e and the minim!m ,ossib"e va"!e of the res!"tant force.
2. A footba"" is 6ic6ed sim!"taneo!s"y by two ,"ayers with force 22& N and 2&& N res,ective"y as shown
in $i!re 2.=. -a"c!"ate the manit!de of the res!"tant force.
22& N
=&&
2&& N
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the resultant force is e"ual to 2ero.
the sum of each component is e"ual to 2ero.
700 70
0
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