SOLUTION Continued
Free body: Frame and pipe 2
0: (15 in.) (56.25 lb)(24 in.) (225 lb)(19.5 in.)0
Ay
MGΣ= − − =
382.5 lb
y
G=
383 lb
y=G
0: 56.25 lb
xx
FAΣ= +
56.25 lb
x
A= −
56.3 lb
x
=A
0: 382.5 lb 225 lb 0
yy
FAΣ= + − =
157.5 lb
y
A= −
157.5
y=A
PROBLEM 6.67
Knowing that each pulley has a radius of 250 mm,
determine the components of the reactions at D and E.
SOLUTION
Free body: Entire assembly:
0: (4.8 kN)(4.25 m) (1.5 m) 0
Ex
MDΣ= − =
13.60 kN
x
D= +
13.60 kN
x=D
0: 13.60 kN 0
xx
FEΣ= + =
13.60 kN
x
E= −
13.60 kN
x=E
0: 4.8 kN 0
y yy
F DEΣ= +− =
(1)
Free body: Member ACE:
0: (4.8 kN)(2.25 m) (4 m) 0
Ay
MEΣ= + =
2.70 kN
y
E= −
2.70 kN
y=E
From Eq. (1):
2.70 kN 4.80 kN 0
y
D−−=
7.50 kN
y
D= +
7.50 kN
y=D
PROBLEM 6.68
Knowing that the pulley has a radius of 75 mm, determine the
components of the reactions at A and B.
SOLUTION
Free body: Entire frame and pulley:
0: (240 N)(75 mm) (600 mm) 0
By
MAΣ= − + =
30.0 N 30.0 N
yy
A=−=A
0: 0 (1)
x xx xx
F BA BAΣ= − = =
0: 30 N 240 N 0
yy
FBΣ= − − =
270 N
y=B
Free body: Member ACD:
0: (200) (30 N)(300) (240 N)(75) 0
Dx
MAΣ= + − =
45.0 N
x
A=
45.0 N
x
=A
From Eq. (1):
45.0 N
Xx
AB= =
45.0 N
x=B
Thus, reactions are
45.0 N
x
=A
,
30.0 N
y=A
45.0 N
x
=B
,
270 N
y=B
PROBLEM 6.69
The cab and motor units of the front–end loader shown are connected by a vertical pin located 2 m behind
the cab wheels. The distance from C to D is 1 m. The center of gravity of the 300–kN motor unit is
located at Gm, while the centers of gravity of the 100–kN cab and 75–kN load are located, respectively, at
Gc and Gl. Knowing that the machine is at rest with its brakes released, determine (a) the reactions at
each of the four wheels, (b) the forces exerted on the motor unit at C and D.
SOLUTION
(a) Free body: Entire machine:
=A
Reaction at each front wheel
=B
Reaction at each rear wheel
0: 75(3.2 m) 100(1.2 m) 2 (4.8 m) 300(5.6 m) 0
A
MBΣ= − + − =
2 325 kNB=
162.5 kN=B
0: 2 325 75 100 300 0
y
FAΣ= + −− − =
2 150 kNA=
75.0 kN=A
SOLUTION Continued
(b) Free body: Motor unit:
(1)
Recalling
0: (1m) 2 (2.8 m) 300(3.6 m) 0
D
MC B
Σ= + − =
1080 5.6CB= −
162.5 kN, 1080 5.6(162.5) 170 kNBC= =−=
170.0 kN=C
0: 170 0
xx
FDΣ= − =
170.0 kN
x
=
D
0: 2(162.5) 300 0
yy
FDΣ= − − =
25.0 kN
y
=D
PROBLEM 6.70
Solve Problem 6.69 assuming that the 75-kN load has been removed.
PROBLEM 6.69 The cab and motor units of the front–end loader shown are connected by a vertical pin
located 2 m behind the cab wheels. The distance from C to D is 1 m. The center of gravity of the 300-kN
motor unit is located at Gm, while the centers of gravity of the 100–kN cab and 75–kN load are located,
respectively, at Gc and Gl. Knowing that the machine is at rest with its brakes released, determine (a) the
reactions at each of the four wheels, (b) the forces exerted on the motor unit at C and D.
SOLUTION
(a) Free body: Entire machine:
PROBLEM 6.71
A trailer weighing 2400 lb is attached to a 2900–lb pickup truck by a ball–and–socket truck hitch at D.
Determine (a) the reactions at each of the six wheels when the truck and trailer are at rest, (b) the
additional load on each of the truck wheels due to the trailer.
SOLUTION
(a) Free body: Trailer:
PROBLEM 6.72
In order to obtain a better weight distribution over the
four wheels of the pickup truck of Problem 6.95, a
compensating hitch of the type shown is used to attach
the trailer to the truck. The hitch consists of two bar
springs (only one is shown in the figure) that fit into
bearings inside a support rigidly attached to the truck.
The springs are also connected by chains to the trailer
frame, and specially designed hooks make it possible to
place both chains in tension. (a) Determine the tension T
required in each of the two chains if the additional load
due to the trailer is to be evenly distributed over the four
wheels of the truck. (b) What are the resulting reactions at
each of the six wheels of the trailer-truck combination?
PROBLEM 6.95 A trailer weighing 2400 lb is attached
to a 2900–lb pickup truck by a ball–and–socket truck hitch
at D. Determine (a) the reactions at each of the six wheels
when the truck and trailer are at rest, (b) the additional
load on each of the truck wheels due to the trailer.
SOLUTION
(a) We small first find the additional reaction
∆
at each wheel due to the trailer.
SOLUTION Continued
Free body: Frame and pipe 2
0: (15 in.) (56.25 lb)(24 in.) (225 lb)(19.5 in.)0
Ay
MGΣ= − − =
382.5 lb
y
G=
383 lb
y=G
0: 56.25 lb
xx
FAΣ= +
56.25 lb
x
A= −
56.3 lb
x
=A
0: 382.5 lb 225 lb 0
yy
FAΣ= + − =
157.5 lb
y
A= −
157.5
y=A
PROBLEM 6.67
Knowing that each pulley has a radius of 250 mm,
determine the components of the reactions at D and E.
SOLUTION
Free body: Entire assembly:
0: (4.8 kN)(4.25 m) (1.5 m) 0
Ex
MDΣ= − =
13.60 kN
x
D= +
13.60 kN
x=D
0: 13.60 kN 0
xx
FEΣ= + =
13.60 kN
x
E= −
13.60 kN
x=E
0: 4.8 kN 0
y yy
F DEΣ= +− =
(1)
Free body: Member ACE:
0: (4.8 kN)(2.25 m) (4 m) 0
Ay
MEΣ= + =
2.70 kN
y
E= −
2.70 kN
y=E
From Eq. (1):
2.70 kN 4.80 kN 0
y
D−−=
7.50 kN
y
D= +
7.50 kN
y=D
PROBLEM 6.68
Knowing that the pulley has a radius of 75 mm, determine the
components of the reactions at A and B.
SOLUTION
Free body: Entire frame and pulley:
0: (240 N)(75 mm) (600 mm) 0
By
MAΣ= − + =
30.0 N 30.0 N
yy
A=−=A
0: 0 (1)
x xx xx
F BA BAΣ= − = =
0: 30 N 240 N 0
yy
FBΣ= − − =
270 N
y=B
Free body: Member ACD:
0: (200) (30 N)(300) (240 N)(75) 0
Dx
MAΣ= + − =
45.0 N
x
A=
45.0 N
x
=A
From Eq. (1):
45.0 N
Xx
AB= =
45.0 N
x=B
Thus, reactions are
45.0 N
x
=A
,
30.0 N
y=A
45.0 N
x
=B
,
270 N
y=B
PROBLEM 6.69
The cab and motor units of the front–end loader shown are connected by a vertical pin located 2 m behind
the cab wheels. The distance from C to D is 1 m. The center of gravity of the 300–kN motor unit is
located at Gm, while the centers of gravity of the 100–kN cab and 75–kN load are located, respectively, at
Gc and Gl. Knowing that the machine is at rest with its brakes released, determine (a) the reactions at
each of the four wheels, (b) the forces exerted on the motor unit at C and D.
SOLUTION
(a) Free body: Entire machine:
=A
Reaction at each front wheel
=B
Reaction at each rear wheel
0: 75(3.2 m) 100(1.2 m) 2 (4.8 m) 300(5.6 m) 0
A
MBΣ= − + − =
2 325 kNB=
162.5 kN=B
0: 2 325 75 100 300 0
y
FAΣ= + −− − =
2 150 kNA=
75.0 kN=A
SOLUTION Continued
(b) Free body: Motor unit:
(1)
Recalling
0: (1m) 2 (2.8 m) 300(3.6 m) 0
D
MC B
Σ= + − =
1080 5.6CB= −
162.5 kN, 1080 5.6(162.5) 170 kNBC= =−=
170.0 kN=C
0: 170 0
xx
FDΣ= − =
170.0 kN
x
=
D
0: 2(162.5) 300 0
yy
FDΣ= − − =
25.0 kN
y
=D
PROBLEM 6.70
Solve Problem 6.69 assuming that the 75-kN load has been removed.
PROBLEM 6.69 The cab and motor units of the front–end loader shown are connected by a vertical pin
located 2 m behind the cab wheels. The distance from C to D is 1 m. The center of gravity of the 300-kN
motor unit is located at Gm, while the centers of gravity of the 100–kN cab and 75–kN load are located,
respectively, at Gc and Gl. Knowing that the machine is at rest with its brakes released, determine (a) the
reactions at each of the four wheels, (b) the forces exerted on the motor unit at C and D.
SOLUTION
(a) Free body: Entire machine:
PROBLEM 6.71
A trailer weighing 2400 lb is attached to a 2900–lb pickup truck by a ball–and–socket truck hitch at D.
Determine (a) the reactions at each of the six wheels when the truck and trailer are at rest, (b) the
additional load on each of the truck wheels due to the trailer.
SOLUTION
(a) Free body: Trailer:
PROBLEM 6.72
In order to obtain a better weight distribution over the
four wheels of the pickup truck of Problem 6.95, a
compensating hitch of the type shown is used to attach
the trailer to the truck. The hitch consists of two bar
springs (only one is shown in the figure) that fit into
bearings inside a support rigidly attached to the truck.
The springs are also connected by chains to the trailer
frame, and specially designed hooks make it possible to
place both chains in tension. (a) Determine the tension T
required in each of the two chains if the additional load
due to the trailer is to be evenly distributed over the four
wheels of the truck. (b) What are the resulting reactions at
each of the six wheels of the trailer-truck combination?
PROBLEM 6.95 A trailer weighing 2400 lb is attached
to a 2900–lb pickup truck by a ball–and–socket truck hitch
at D. Determine (a) the reactions at each of the six wheels
when the truck and trailer are at rest, (b) the additional
load on each of the truck wheels due to the trailer.
SOLUTION
(a) We small first find the additional reaction
∆
at each wheel due to the trailer.