PROBLEM 6.82
See solution on the next page…
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SOLUTION
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PROBLEM 6.83
Two rods are connected by a frictionless collar B. Knowing that the magnitude
of the couple MA is 500 lb ∙ in., determine (a) the couple MC required for
equilibrium, (b) the corresponding components of the reaction at C.
SOLUTION
PROBLEM 6.84
Two rods are connected by a frictionless collar B. Knowing that the
magnitude of the couple MA is 500 lb ∙ in., determine (a) the couple MC
required for equilibrium, (b) the corresponding components of the reaction
at C.
SOLUTION
PROBLEM 6.85
The pliers shown are used to grip a 0.3–in.–diameter rod.
Knowing that two 60–lb forces are applied to the handles,
determine (a) the magnitude of the forces exerted on the
rod, (b) the force exerted by the pin at A on portion AB of
the pliers.
SOLUTION
Free body: Portion AB:
(a)
(b)
0: (1.2 in.) (60 lb)(9.5 in.) 0
A
MQΣ= − =
475 lbQ=
0: (sin30 ) 0
xx
FQ AΣ = °+ =
(475 lb)(sin30 ) 0
x
A°+ =
237.5 lb
x
A= −
237.5 lb
x
=A
0: (cos30 ) 60 lb 0
yy
FQ AΣ = − °+ − =
(475 lb)(cos30 ) 60 lb 0− °+ − =
y
A
471.4 lb
y
A= +
471.4 lb
y
=A
528 lb=A
63.3°
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PROBLEM 6.86
In using the bolt cutter shown, a worker applies two 300–N
forces to the handles. Determine the magnitude of the
forces exerted by the cutter on the bolt.
SOLUTION
FBD cutter AB: FBD handle BC:
I Dimensions in mm II
FBD I:
0: 0
xx
FBΣ= =
FBD II:
0: (12 mm) (448 mm)300 N 0
Cy
MBΣ= − =
11,200.0 N
y
B=
Then
FBD I:
0: (96 mm) (24 mm) 0
Ay
M BFΣ= − =
4
y
FB=
44,800 N 44.8 kNF= =
Copyright © McGraw–Hill Education. All rights reserved. No reproduction or distribution without the prior written
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PROBLEM 6.87
The garden shears shown consist of two blades and two handles. The two handles are connected by pin C and
the two blades are connected by pin D. The left blade and the right handle are connected by pin A; the right
blade and the left handle are connected by pin B. Determine the magnitude of the forces exerted on the small
branch at E when two 80-N forces are applied to the handles as shown.
SOLUTION
By symmetry vertical components Cy, Dy, Ey are 0. Then by considering
0
y
FΣ=
on the blades or handles,
we find that Ay and By are 0.
Free body: Right handle
0: (30 mm) (80 N)(270 mm) 0
C
MAΣ= − =
720 N
A= +
0: 720 N 80 N 0
x
FCΣ= − − =
800 NC= +
Free body: Left blade
0: (180 mm) (720 N)(60 mm) 0
D
MEΣ= − =
240 NE=
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PROBLEM 6.88
A hand–operated hydraulic cylinder has been designed for use where space is severely limited. Determine the
magnitude of the force exerted on the piston a D when two 90-lb forces are applied as shown.
SOLUTION
()
() ( ) 1.2( ) (1)
2 in. 2.4 in.
CD y
CD x CD y CD x
F
FFF= =
0:( ) (4 in.) ( ) (1.5 in.) (90 lb)(13.2 in.) = 0
Substituting from (1) for ( )
1.2( ) (4 in.) ( ) (1.5 in.)=(90 lb)(13.2 in.) = 0
A CD y CD x
CD y
CD x CD x
MF F
F
FF
= −−
−
∑
( ) 360 lb
CD x
F=
Force exerted on piston:
Because of symmetry:
Resultant force is:
2( ) 2 (360 lb)
DE CD
CD x
FF
DF
=
= =
D=720 lb
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PROBLEM 6.89
of two parts EDC and CDB hinged at C and bearing against each
other at D. Determine the force P required to release the brace.
SOLUTION
Free body: Shelf:
0: (10 in.) (45 lb)(6.25 in.) 0
Ay
MBΣ= − =
28.125 lb
y
B=
Free body: Portion ECB:
0: (7.5 in.) (7.5 in.) (28.125 lb)(10 in.) 0
Ex
MB PΣ= − − − =
37.5
x
BP=−−
Free body: Portion CDB:
0: (28.125 lb)(4.6 in.) (2.2 in.) 0
Cx
MBΣ= − − =
(28.125 lb)(4.6 in.) ( 37.5 )(2.2 in.) 0P− −− − =
21.3 lbP=
21.3 lb=P
consent of McGraw–Hill Education.
PROBLEM 6.82
See solution on the next page…
consent of McGraw–Hill Education.
SOLUTION
consent of McGraw–Hill Education.
PROBLEM 6.83
Two rods are connected by a frictionless collar B. Knowing that the magnitude
of the couple MA is 500 lb ∙ in., determine (a) the couple MC required for
equilibrium, (b) the corresponding components of the reaction at C.
SOLUTION
PROBLEM 6.84
Two rods are connected by a frictionless collar B. Knowing that the
magnitude of the couple MA is 500 lb ∙ in., determine (a) the couple MC
required for equilibrium, (b) the corresponding components of the reaction
at C.
SOLUTION
PROBLEM 6.85
The pliers shown are used to grip a 0.3–in.–diameter rod.
Knowing that two 60–lb forces are applied to the handles,
determine (a) the magnitude of the forces exerted on the
rod, (b) the force exerted by the pin at A on portion AB of
the pliers.
SOLUTION
Free body: Portion AB:
(a)
(b)
0: (1.2 in.) (60 lb)(9.5 in.) 0
A
MQΣ= − =
475 lbQ=
0: (sin30 ) 0
xx
FQ AΣ = °+ =
(475 lb)(sin30 ) 0
x
A°+ =
237.5 lb
x
A= −
237.5 lb
x
=A
0: (cos30 ) 60 lb 0
yy
FQ AΣ = − °+ − =
(475 lb)(cos30 ) 60 lb 0− °+ − =
y
A
471.4 lb
y
A= +
471.4 lb
y
=A
528 lb=A
63.3°
Copyright © McGraw–Hill Education. All rights reserved. No reproduction or distribution without the prior written
consent of McGraw–Hill Education.
PROBLEM 6.86
In using the bolt cutter shown, a worker applies two 300–N
forces to the handles. Determine the magnitude of the
forces exerted by the cutter on the bolt.
SOLUTION
FBD cutter AB: FBD handle BC:
I Dimensions in mm II
FBD I:
0: 0
xx
FBΣ= =
FBD II:
0: (12 mm) (448 mm)300 N 0
Cy
MBΣ= − =
11,200.0 N
y
B=
Then
FBD I:
0: (96 mm) (24 mm) 0
Ay
M BFΣ= − =
4
y
FB=
44,800 N 44.8 kNF= =
Copyright © McGraw–Hill Education. All rights reserved. No reproduction or distribution without the prior written
consent of McGraw–Hill Education.
PROBLEM 6.87
The garden shears shown consist of two blades and two handles. The two handles are connected by pin C and
the two blades are connected by pin D. The left blade and the right handle are connected by pin A; the right
blade and the left handle are connected by pin B. Determine the magnitude of the forces exerted on the small
branch at E when two 80-N forces are applied to the handles as shown.
SOLUTION
By symmetry vertical components Cy, Dy, Ey are 0. Then by considering
0
y
FΣ=
on the blades or handles,
we find that Ay and By are 0.
Free body: Right handle
0: (30 mm) (80 N)(270 mm) 0
C
MAΣ= − =
720 N
A= +
0: 720 N 80 N 0
x
FCΣ= − − =
800 NC= +
Free body: Left blade
0: (180 mm) (720 N)(60 mm) 0
D
MEΣ= − =
240 NE=
consent of McGraw–Hill Education.
PROBLEM 6.88
A hand–operated hydraulic cylinder has been designed for use where space is severely limited. Determine the
magnitude of the force exerted on the piston a D when two 90-lb forces are applied as shown.
SOLUTION
()
() ( ) 1.2( ) (1)
2 in. 2.4 in.
CD y
CD x CD y CD x
F
FFF= =
0:( ) (4 in.) ( ) (1.5 in.) (90 lb)(13.2 in.) = 0
Substituting from (1) for ( )
1.2( ) (4 in.) ( ) (1.5 in.)=(90 lb)(13.2 in.) = 0
A CD y CD x
CD y
CD x CD x
MF F
F
FF
= −−
−
∑
( ) 360 lb
CD x
F=
Force exerted on piston:
Because of symmetry:
Resultant force is:
2( ) 2 (360 lb)
DE CD
CD x
FF
DF
=
= =
D=720 lb
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PROBLEM 6.89
of two parts EDC and CDB hinged at C and bearing against each
other at D. Determine the force P required to release the brace.
SOLUTION
Free body: Shelf:
0: (10 in.) (45 lb)(6.25 in.) 0
Ay
MBΣ= − =
28.125 lb
y
B=
Free body: Portion ECB:
0: (7.5 in.) (7.5 in.) (28.125 lb)(10 in.) 0
Ex
MB PΣ= − − − =
37.5
x
BP=−−
Free body: Portion CDB:
0: (28.125 lb)(4.6 in.) (2.2 in.) 0
Cx
MBΣ= − − =
(28.125 lb)(4.6 in.) ( 37.5 )(2.2 in.) 0P− −− − =
21.3 lbP=
21.3 lb=P
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