Uniform Contact Forces
What bodies interact with Block B?
A
6 lb
B
8 lb
C
10 lb
Table
Block A?
Block C?
Yes
No
Yes
No
Gr
Pi
Gr
Pi
Table?
Yes
No
Gr
Pi
Earth?
Yes
No
Gr
Pi
Uniform Contact Forces
Block A, block C and earth interact with block B.
A
6 lb
B
8 lb
B
C
10 lb
Table
Are the magnitudes of these forces known?
(without using equilibrium)
Block A on B?
Yes
No
Gr
Pi
Block C on B?
Yes
No
Gr
Pi
Earth on B?
Yes
No
Gr
Pi
Uniform Contact Forces
A
6 lb
B
B
8 lb
C
10 lb
Table
The only force known without using equilibrium is due to gravity.
Give symbols to the contact forces between blocks (equal and opposite):
Force of B on A
B
A
NAB
NBC
Force of A on B NAB
NBC
B
C
Uniform Contact Forces
A
6 lb
B
8 lb
C
10 lb
Table
Free body diagram of B:
NAB
8 lb
NBC
B
Uniform Contact Forces
A
6 lb
B
8 lb
C
10 lb
Table
Are these free body diagrams of A, B and C correct?
NAB
6 lb
NAB
8 lb
10 lb
8 lb
NBC
Yes
No
Ntable
Gr
Pi
Uniform Contact Forces
6 lb
8 lb
A
B
C
10 lb
Table
Correct free body diagrams are:
6 lb
NAB
ΣFy = NAB - 6 = 0
NAB = 6 lb
NAB
NBC
8 lb
10 lb
NBC
Ntable
ΣFy = - NAB - 8 + NAB = 0
ΣFy = - NBC - 10 + Ntable = 0
NBC = 14 lb
Ntable = 24 lb
Uniform Contact Forces
A
6 lb
B
8 lb
C
10 lb
Table
FBD of A
6 lb
NAB
FBD of B
NAB
6 lb
8 lb
8 lb
10 lb
NBC
NBC
FBD of C
10 lb
Ntable
Ntable
FBD of A, B, and C as a unit
Uniform Contact Forces
What bodies interact with Blocks B and C as a pair?
E
D
C
C
B
B
A
Table
Block A?
Block D?
Block E?
Yes
No
Yes
No
Yes
No
Gr
Pi
Gr
Pi
Gr
Pi
Table?
Yes
No
Gr
Pi
Earth?
Yes
No
Gr
Pi
Uniform Contact Forces
Is this the correct free body diagram of B and C as a unit?
E
(Blocks B and C are enlarged)
D
C
WD
B
A
C
WC
NBC
B
Yes
No
Gr
Pi
WB
NAB
Uniform Contact Forces
How many errors there are in this FBD of B and C as a unit?
E
(Blocks B and C are enlarged)
D
WD
C
B
WC
C
A
NBC
WB
B
NAB
1
Pi
2 Bl
3 Ye
4
Wh
Uniform Contact Forces
WD
E
C
D
NBC
C
B
WC
B
WB
A
NAB
Errors:
WD is force of earth on D (not D on C) should not be in the diagram
NDC is needed instead
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
Uniform Contact Forces
FBD of B and C as a unit
E
NCD
D
C
B
A
C
B
WC
WB
NAB
Uniform Contact Forces
Block is supported by a cord which exerts force on it through a washer :
T cord on washer
T cord on washer
T block on washer
T block on washer
T washer on block
T washer on block
WB
WB
Force T exerted by the washer on block is equal the tension in the cord
Uniform Contact Forces
1
Blocks rest on each other and
are connected by cords.
C
B
2
A
• cord exerts force on this block
through a washer
• cord passes through hole in this
block and exerts no force on it
Uniform Contact Forces
1
All blocks have equal weight W.
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.
C
B
2
A
Determine tensions in cords 1 and 2,
and forces between contacting blocks
Uniform Contact Forces
Is this the correct FBD
of block B?
1
WC
C
B
B
WB
T2
T1
T1
2
A
Yes
No
Gr
Pi
T
T2 2
Uniform Contact Forces
Which of the forces in this
FBD of block B are shown
correctly?
1
WC
C
B
WB
T2
B
T1
2
Yes
WC
No
Gr
Yes
No
Gr
Pi
T2
T1
Yes
WB
No
Gr
Yes
T2
No
Gr
Pi
A
T1
Pi
Pi
Uniform Contact Forces
1
This is the correct
FBD of block B
NBC
C
B
WB
B
T1
T1
2
WC
A
B
WB
T2
T1
T1
T2
Uniform Contact Forces
Draw the FBD’s of each
block A, B and C separately
1
C
C
B
B
2
A
A
Uniform Contact Forces
C
WC
T2
1
T2
NBC
NBC
C
WB
B
B
T1
2
A
T2
T1
WA
T2
A
Block A: T2 = W/2
Block C: NBC = 2W
Block B: T1 = 3W/2
Uniform Contact Forces
1
C
B
2
A
Draw the FBD of:
blocks A, B, C and cord 2,
as one unit.
Uniform Contact Forces
1
FBD of blocks A, B and C
and cord 2 as one unit
WC
C
WB
B
T1
T1
2
A
WA
ΣFy = - 3W + 2T1 = 0
T1 = 3W/2