# MOMEN DAN KOPEL - · PDF fileApa itu momen gaya ? The moment of a force about a point provides a measure of the tendency for rotation (sometimes called a torque). MOMENT IN 2-D (continued)

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MO

ME

N D

AN

KO

PE

L

Apa y

ang d

ipela

jari

sekara

ng ?

Me

ng

eta

hu

i d

an m

em

ah

am

i m

aksud d

ari

mom

en g

aya,

mom

en k

ope

l, d

an c

ara

mem

ind

ah g

aya

Apa itu

mo

men

gaya ?

The

mo

men

t of

a fo

rce

a poin

t pro

vid

es a

mea

sure

of

the

tenden

cy f

or

rota

tion (

som

etim

es c

alle

d a

torq

ue)

.

MO

ME

NT

IN

2-D

(co

nti

nued

)

In t

he

2-D

cas

e, t

he

mag

nit

ude

of

the

mo

men

t is

Mo =

F d

As

show

n, d

is

the

per

pen

dic

ula

r dis

tance

fro

m p

oin

t O

to t

he

line

of

acti

on o

f th

e fo

rce.

In 2

-D, th

e dir

ecti

on o

f M

O i

s ei

ther

clo

ckw

ise

or

counte

r-cl

ock

wis

e dep

endin

g o

n t

he

tenden

cy f

or

rota

tion.

Mo

me

nt

in 2

-D

b O d

a F

b

O

a

F y

F

F x

As

show

n, d

is

the

per

pen

dic

ula

r dis

tance

fro

m p

oin

t O

to t

he

line

of

acti

on o

f th

e fo

rce.

MO =

F d

and t

he

dir

ecti

on i

s co

unte

r-cl

ock

wis

e.

Oft

en i

t is

eas

ier

to

det

erm

ine

MO b

y u

sing t

he

com

ponen

ts o

f F

as

sho

wn.

MO =

(F

Y a

) (

FX b

)

CC

W =

(+

)

CW

=

(-)

Exam

ple

1G

iven

: A

40 N

forc

e is

appli

ed t

o t

he

wre

nch

.

Fin

d:

The

mo

men

t of

the

forc

e at

O.

Pla

n:

1)

Res

olv

e th

e fo

rce

along x

and y

axes

.

2)

Det

erm

ine

MO u

sing

scal

ar a

nal

ysi

s.

Solu

tion

: +

F

y =

- 4

0 c

os

20

N

+

Fx =

- 4

0 s

in 2

0

N

+ M

O =

{-(

40 c

os

20)

(200)

+ (

40 s

in 2

0)

(30)}

Nm

m=

-7107 N

mm

= -

7.1

1 N

m

EX

AM

PL

E 2

Giv

en

: A

400 N

forc

e is

appli

ed t

o t

he

fram

e

and

= 2

0.

Fin

d:

The

mo

men

t of

the

forc

e at

A.

Pla

n:

1)

Res

olv

e th

e fo

rce

along x

and y

axes

.

2)

Det

erm

ine

MA u

sing s

cala

r an

alysi

s.

EX

AM

PL

E 2

(co

nti

nued

)

Solu

tion

+

Fy =

-400 c

os

20

N

+

Fx =

-400 s

in 2

0

N

+ M

A =

{(4

00 c

os

20)

(2)

+ (

400 s

in 2

0)

(3)}

Nm

= 1

160 N

m

CO

NC

EP

T Q

UE

ST

ION

1.

What

is

the

mo

men

t of

the

10 N

forc

e

poin

t A

(M

A)?

A)

10 N

m

B

) 30 N

m C

) 13 N

m

D)

(10/3

) N

m E

) 7 N

m

F =

10 N

A

d=

3m

2. If

a f

orc

e of

mag

nit

ude

F c

an b

e ap

pli

ed i

n f

our

dif

fere

nt

2-D

confi

gura

tions

(P,Q

,R,

& S

), s

elec

t th

e ca

ses

resu

ltin

g i

n t

he

max

imu

m a

nd m

inim

um

torq

ue

val

ues

on t

he

nut.

(M

ax, M

in).

A)

(Q, P

)

B

) (R

, S

)

C)

(P, R

)

D

) (Q

, S

)

P Q

S

R

10 N

3m

P

2m

5N

3. U

sing t

he

CC

W d

irec

tion a

s posi

tive,

the

net

mo

men

t of

the

two f

orc

es a

bout

poin

t P

is

A)

10 N

m

B

) 20 N

m

C

) -

20 N

m

D)

40 N

m

E

) -

40 N

m

Apa itu

mo

men

kopel ?

Mo

me

nt

of

a C

ouple

A c

ouple

is

def

ined

as

two

par

alle

l fo

rces

wit

h t

he

sam

e

mag

nit

ude

but

opposi

te i

n

dir

ecti

on s

epar

ated

by a

per

pen

dic

ula

r dis

tance

d.

The

mo

men

t of

a co

uple

is

def

ined

as

MO =

F d

(usi

ng a

sca

lar

anal

ysi

s) o

r as

MO =

r F

(usi

ng a

vec

tor

anal

ysi

s).

Her

e r

is a

ny p

osi

tion v

ecto

r fr

om

the

line

of

acti

on o

f

F

to t

he

line

of

acti

on o

f F

.

Pro

ble

m S

olv

ing

A

B

A t

orq

ue

or

mo

men

t of

12 N

m

is

requir

ed t

o r

ota

te t

he

whee

l.

Whic

h o

ne

of

the

two g

rips

of

the

whee

l ab

ove

wil

l re

quir

e le

ss

forc

e to

rota

te t

he

whee

l?

Pro

ble

m S

olv

ing (

2-D

)

A

B

M=

Fd

12 =

F 0

.4

F =

30 N

M=

Fd

12 =

F 0

.3

F =

40 N

PR

OB

LE

M S

OL

VIN

G -

SC

AL

AR

Giv

en

: T

wo c

ouple

s ac

t on t

he

bea

m. T

he

resu

ltan

t co

uple

is

zero

.

Fin

d:

The

mag

nit

udes

of

the

forc

es

P a

nd F

and t

he

dis

tance

d.

PL

AN

:

1)

Use

def

init

ion o

f a

couple

to f

ind P

and F

.

2)

Res

olv

e th

e 300 N

forc

e in

x

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