Force 2.9 Student Copy

8/17/2019 Force 2.9 Student Copy

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2.9 Equilibrium of Force


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2.9 Equ!"rum o# For$%

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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


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


the resultant force is e"ual to 2ero.

the sum of each component is e"ual to 2ero.

700 70

0

Force 2.9 Student Copy

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