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8/2/2019 Diagrama de Corpo Livre
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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
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Introduction to FBDs
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
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Introduction to FBDs
6 lb
8 lb
10 lb
A
B
C
Table
B
Draw Free Body Diagram of B:
B
NAB
NBC
8 lb
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Introduction to FBDs
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:
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Introduction to FBDs
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
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Introduction to FBDs
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
8/2/2019 Diagrama de Corpo Livre
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Introduction to FBDs
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
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Introduction to FBDs
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
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Introduction to FBDs
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
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Introduction to FBDs
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
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Introduction to FBDs
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
8/2/2019 Diagrama de Corpo Livre
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Introduction to FBDs
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
Introduction to FBDs
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Introduction to FBDs
correct FBD of B and C as a unit
E
D
C
B
A
WB
NAB
NCD
WCC
B
Introduction to FBDs
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Introduction to FBDs
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:
=
=
Introduction to FBDs
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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
Introduction to FBDs
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Introduction to FBD s
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
Introduction to FBDs
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Introduction to FBD s
Is this the correct FBD
of block B?1
2
A
B
C
Yes
No
Gr
Pi
T2
T1 T1
WC
T2BWB
T2
Introduction to FBDs
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Introduction to FBD s
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
Introduction to FBDs
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Introduction to FBD s
1
2
A
B
C
T1 T1
WC
T2
T2WB
B
T1 T1
WB
NBC
This is the correct
FBD of block B
B
Introduction to FBDs
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Introduction to FBD s
1
2
A
B
C
Draw the FBDs of each
block A, B and C separately
A
B
C
Introduction to FBDs
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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
Introduction to FBDs
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1
2
A
B
C
Draw the FBD of:
blocks A, B, C and cord 2,
as one unit.
Introduction to FBDs
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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
Introduction to FBDs
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Introduction to FBDs
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