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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
consent of McGraw-Hill Education.
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
consent of McGraw-Hill Education.
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.
