18046_Lecture Notes 3.1 - 3.3

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Mechanics for Engineers: Statics, 13th SI EditionR. C. Hibbeler and Kai Beng Yap

© Pearson Eduation South !sia Pte "td#$13. !ll rights reser%ed.

EQUILIBRIUM OF A PARTICLE, THE FREE-BODYDIAGRAM & COPLANAR FORCE SYSTEMS

In-Class Actiiti!s&

• Reading 'ui(

• !ppliations

• )hat, )h*, and Ho+

o a -B• E/uations oE/uilibriu0

• !nal*sis o Springand Pulle*s

• Conept 'ui(

• roup Proble0Sol%ing

• !ttention 'ui(

T"#a$%s O'!cti!s&

Students +ill be able to &

a2 ra+ a reebod* diagra0 4-B2,and,

b2 !ppl* e/uations o e/uilibriu0 to

sol%e a # proble0.

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READING QUI(

12 )hen a partile is in e/uilibriu0, the su0 o ores atingon it e/uals 555 . 4Choose the 0ost appropriate ans+er2

!2 ! onstant B2 ! positi%e nu0ber C2 6ero

2 ! negati%e nu0ber E2 !n integer

#2 -or a ritionless pulle* and able, tensions in theable 471 and 7#2 are related as 55555 .

!2 71 8 7#

B2 71 9 7#

C2 71 : 7#

2 71 9 7# sin θ

T 1

T 2

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7he rane is liting a load. 7odeide i the straps holding theload to the rane hoo; +ill ail,*ou need to ;no+ the ore inthe straps. Ho+ ould *ou indthe ores<

APPLICATIONS

Straps

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-or a spool o gi%en+eight, ho+ +ould *ouind the ores in ables!B and !C< I designinga spreader bar li;e this

one, *ou need to ;no+the ores to 0a;e surethe rigging doesn=t ail.

APPLICATIONS 4ontinued2

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APPLICATIONS 4ontinued2

-or a gi%en ore e>erted on the boat=s to+ing pendant, +hat arethe ores in the bridle ables< )hat si(e o able 0ust *ou use<

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COPLANAR FORCE SYSTEMS4Setion 3.32

7o deter0ine the tensions inthe ables or a gi%en +eight

o *linder, *ou need tolearn ho+ to dra+ a reebod* diagra0 and appl* thee/uations o e/uilibriu0.

7his is an e>a0ple o a # oroplanar ore s*ste0.

I the +hole asse0bl* is ine/uilibriu0, then partile ! is

also in e/uilibriu0.

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THE )HAT, )HY, AND HO) OF AFREE-BODY DIAGRAM *FBD+

-reebod* diagra0s are one o the 0ost i0portant things or*ou to ;no+ ho+ to dra+ and use or statis and other sub?ets@

)at It is a dra+ing that sho+s all e>ternal ores

ating on the partile.

)$ It is .!$ to being able to +rite the e/uations oe/uilibriu0A+hih are used to sol%e or the un;no+ns4usuall* ores or angles2.

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H"/?

!ti%e ores& 7he* +ant to 0o%e the partile.Reati%e ores& 7he* tend to resist the 0otion.

ote & C*linder 0ass 9 $ Kg

1. I0agine the partile to be isolated or ut ree ro0 itssurroundings.

A

3. Identi* eah ore and sho+ all ;no+n 0agnitudes anddiretions. Sho+ all un;no+n 0agnitudes and D ordiretions as %ariables.

FC 0 12345 N *)at is tis+

FB

FD

30˚

#. Sho+ all the ores that at on the partile.

-B at !

A

y

x

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EQUATIONS OF 3-D EQUILIBRIUM

r, +ritten in a salar or0,Σ -> 9 $ and Σ -* 9 $

7hese are t+o salar e/uations o e/uilibriu0 4EoE2.7he* an be used to sol%e or up to t+o un;no+ns.

Sine partile ! is in e/uilibriu0, the

net ore at ! is (ero.So F B F F C F F D 9 $

or Σ F 9 $

FBD at A

A

In general, or a partile in e/uilibriu0,

Σ F 9 $ or Σ -> i 6 Σ -* j 9 $ 9 $ i F $ j 4a %etor e/uation2

-B at !

A

FB

FDA

FC 0 12345 N

y

x30˚

-B at !

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)rite the salar EoE&

F → Σ -> 9 -B os 3$G - 9 $

F ↑ Σ -* 9 -B sin 3$G 3#. 9 $

Sol%ing the seond e/uation gi%es& -B 9 JL →

-ro0 the irst e/uation, +e get& - 9 M$ ←

ote & C*linder 0ass 9 $ Kg

FBD at A

A

FB

FDA

FC 0 12345 N

y

x30˚

EQUATIONS OF 3-D EQUILIBRIUM 4ontinued2

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SIMPLE SPRINGS

Spring -ore 9 spring onstant N deor0ation o spring

or - 9 ; N s

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CABLES AND PULLEYS

)ith a ritionless pulle* and able

71 9 7#.

T 1

T 2

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E7AMPLE

Plan8

1. ra+ a -B or point !.

#. !ppl* the EoE to sol%e or the ores in ropes !Band !C.

Gi!n8 7he bo> +eighs LL$ andgeo0etr* is as sho+n.

Fin#8 7he ores in the ropes !Band !C.

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E7AMPLE 4ontinued2

-B at point !FCFB

A

FD 0 99: N

y

x30˚

3

4

5

!ppl*ing the salar EoE at !, +e getO

F → ∑ - > 9 -B os 3$ -C 4DL2 9 $

F → ∑ - * 9 -B sin 3$ F -C 43DL2 LL$ 9 $

Sol%ing the abo%e e/uations, +e getO

-B 9 J and -C 9 L1

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CONCEPT QUESTIONS

1$$$ 1$$$

1$$$

4 ! 2 4 B 2 4 C 2

12 !ssu0ing *ou ;no+ the geo0etr* o the ropes, *ou annotdeter0ine the ores in the ables in +hih s*ste0 abo%e<

!2 7he +eight is too hea%*.

B2 7he ables are too thin.

C2 7here are 0ore un;no+ns than e/uations.

2 7here are too e+ ables or a 1$$$ +eight.

#2 )h*<

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GROUP PROBLEM SOL;ING

1. ra+ a -B or Point .

#. !ppl* EoE at Point to sol%e or the un;no+ns 4-C

Q -E

2.

3. Kno+ing -C, repeat this proess at point C.

Gi!n8 7he 0ass o la0p is #$;g and geo0etr* is as

sho+n.Fin#8 7he ore in eah able.

Plan8

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GROUP PROBLEM SOL;ING 4ontinued2

!ppl*ing the salar EoE at , +e getO

F↑ ∑ -* 9 -E sin 3$ #$ 4.12 9 $

F→ ∑ -> 9 -E os 3$ -C 9 $

Sol%ing the abo%e e/uations, +e get&

-E 9 3# and -C 9 3$

-B at point

FDE

FCD

D

) 0 3: *24

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GROUP PROBLEM SOL;ING 4ontinued2

!ppl*ing the salar EoE at C, +e getO

F→ ∑ -> 9 3$ -BC sin L -!C 43DL2 9 $

F ↑ ∑ -* 9 -!C 4DL2 -BC os L 9 $

Sol%ing the abo%e e/uations, +e getO

-BC 9 #JL and -!C 9 #3

-B at point C

FCD 93$

FAC

C

y

x

45˚

FBC

3

45

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ATTENTION QUI(

!

3$°

$°

1$$

1. Selet the orret -B o partile !.

!2 A

1$$

B2

3$°

$°

!

-1 -#

C2 30°A

F

1$$

3$° $°

-1-#

1$$

2

!

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ATTENTION QUI(

-#

-1

C

L$°

#. sing this -B o Point C, the su0 o

ores in the >diretion 4Σ -2 is 555 .

se a sign on%ention o F → .

!2 -# sin L$ #$ 9 $

B2 -# os L$ #$ 9 $

C2 -# sin L$ -1 9 $

2 -# os L$ F #$ 9 $

#$

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Mechanics for Engineers: Statics, 13th SI EditionR C Hibbeler and Kai Beng Yap

© Pearson Eduation South !sia Pte "td#$13 !ll rights reser%ed

End of the Lecture

Let Learning Continue

18046_Lecture Notes 3.1 - 3.3

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