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8/2/2019 Diagrama de Corpo Livre

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Introduction to FBDs

What bodies interact with BlockC?

Yes

No

Gr

Pi

Block A?

Yes

No

Gr

Pi

Block B?

Yes

No

Gr

Pi

Table?

Yes

No

Gr

Pi

Earth?

6 lb

8 lb

10 lb

AB

C

Table


3/27


What bodies interact with BlockB?

Yes

No

Gr

Pi

Block A?

Yes

No

Gr

Pi

Block C?

Yes

No

Gr

Pi

Table?

Yes

No

Gr

Pi

Earth?

6 lb

8 lb

10 lb

AB

C

Table


4/27


6 lb

8 lb

10 lb

A

B

C

Table

B

Draw Free Body Diagram of B:

B

NAB

NBC

8 lb


5/27


6 lb

8 lb

10 lb

A

B

C

Table

B

The only force that has known magnitude is the force of gravity!

(without using equilibrium)

Recall how to label the unknown contact forces between blocks (equal and opposite):

A

BNAB

NAB

B

C

NBC

NBCforce of B on A

force of A on B

force of C on B

force of B on C

Draw Free Body Diagram of B:


6/27


6 lb

8 lb

10 lb

A

B

C

Table

Are these free body diagrams of A, B and C correct?

NAB

NBC

8 lb

8 lb

NAB

6 lb 10 lb

Ntable

Yes

No

Gr

Pi


7/27


6 lb

8 lb

10 lb

A

B

C

Table

Here are the errors:

NAB

NBC

8 lb

8 lb

NAB

6 lb 10 lb

Ntable


8/27


6 lb

8 lb

10 lb

A

B

C

Table

Correct free body diagrams are:

NAB

NBC

8 lb

NBC

NAB

6 lb 10 lb

Ntable

Fy = NAB - 6 = 0

NAB = 6 lb

Fy = - NAB - 8 + NBC = 0

NBC = 14 lb

Fy = - NBC - 10 + Ntable = 0

Ntable = 24 lb


9/27


6 lb

8 lb

10 lb

A

B

C

Table

NAB

NBC

8 lb

NAB

6 lb

NBC

10 lb

Ntable

FBD of A, B, and C as a unit

6 lb8 lb

10 lb

Ntable

FBD of A

FBD of C

FBD of B

I d i FBD


10/27


What bodies interact with Blocks B and C as a pair?

Table

Yes

No

Gr

Pi

Block A?

Yes

No

Gr

Pi

Block D?

Yes

No

Gr

Pi

Table?

Yes

No

Gr

Pi

Earth?

Yes

No

Gr

Pi

Block E?

E

D

C

B

A

C

B

I t d ti t FBD


11/27


Is this the correct free body diagram of B and C as a unit?

WB

NAB

WD

WC

NBC

(Blocks B and C are enlarged)E

D

C

B

A

Yes

No

Gr

Pi

C

B

I t d ti t FBD


12/27


How many errors there are in this FBD of B and C as a unit?

WB

NAB

WD

WC

NBC

1 Pi 2 3 4YeBl Wh

E

D

C

B

A

C

B

(Blocks B and C are enlarged)

I t d ti t FBD


13/27


WB

NAB

WD

WC

NBC

WD - force of earth on D should not be in the diagramNDC - force of D on C needed

NBC which acts between bodies B and C should not be in the diagram

only forces exerted by other bodies on [B and C] as a unit are to be in the FBD

Errors:

E

D

C

B

A

C

B

NDC



14/27


correct FBD of B and C as a unit

E

D

C

B

A

WB

NAB

NCD

WCC

B



15/27


WB

NWB

Block is supported by a cord which exerts force on it through a washer :

TNWB NWBT

Force NWB exerted by the washer on block is equal to the tension T in the cord:

WB

NWB

WB

T

FBDs:

=

=



16/27

Introduction to FBD s

Blocks rest on each other and

are connected by cords.

cord exerts force on this block

through a washer

cord passes through hole in this

block and exerts no force on it

1

2

A

B

C



17/27


All blocks have equal weight W.

Determine tensions in cords 1 and 2,and forces between contacting blocks

Each pair of cords (e.g., pair 1 or pair

2) is located symmetrically about

vertical centerline so both cords in a

pair have the same tension.

1

2

A

B

C



18/27


Is this the correct FBD

of block B?1

2

A

B

C

Yes

No

Gr

Pi

T2

T1 T1

WC

T2BWB

T2



19/27


Which of the forces in this

FBD of block B are correct?1

2

A

B

C

Yes

No

Gr

Pi

WCYes

No

Gr

Pi

WB

YesNo

Gr

Pi

T1 Yes

No

Gr

Pi

T2

T1 T1

WC

BT2

T2

WB



20/27


1

2

A

B

C

T1 T1

WC

T2

T2WB

B

T1 T1

WB

NBC

This is the correct

FBD of block B

B



21/27


1

2

A

B

C

Draw the FBDs of each

block A, B and C separately

A

B

C



22/27

1

2

A

B

C

T1 T1

NBC

WC

NBC

T2T2

WAT2 T2

Block A: T2 = W/2 Block C: NBC = 2W

WB

Block B: T1 = 3W/2

A

B

C



23/27

1

2

A

B

C

Draw the FBD of:

blocks A, B, C and cord 2,

as one unit.



24/27

1

2

A

B

CW

C

WA

WB

T1 T1

FBD of blocks A, B and C

and cord 2 as one unit

Fy = - 3W + 2T1 = 0 T1 = 3W/2



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