Statics 2e 665
Problem 5.32
A motor and mounting hardware with weight
WD65 lb
are supported by
rollers
A
,
B
,
C
, and
D
. Each pair of rollers is loose-fitting so that only one
roller of the pair will make contact with the fixed rail. This problem may be
idealized as two-dimensional if the torque the motor applies to the pulleys is
neglected. Determine which rollers make contact and the reactions at these
rollers if:
PD0and QD125 lb.
Problem 5.33
A motor and mounting hardware with weight
WD65 lb
are supported by
rollers
A
,
B
,
C
, and
D
. Each pair of rollers is loose-fitting so that only one
roller of the pair will make contact with the fixed rail. This problem may be
idealized as two-dimensional if the torque the motor applies to the pulleys is
neglected. Determine which rollers make contact and the reactions at these
rollers if:
PD200 lb and QD0.
Problem 5.34
A motor and mounting hardware with weight
WD65 lb
are supported by
rollers
A
,
B
,
C
, and
D
. Each pair of rollers is loose-fitting so that only one
roller of the pair will make contact with the fixed rail. This problem may be
idealized as two-dimensional if the torque the motor applies to the pulleys is
neglected. Determine which rollers make contact and the reactions at these
rollers if:
PD200 lb and QD125 lb.
Problem 5.35
During assembly in a factory, a compressor with weight
WD120 lb
rests on a
bench. A cover plate is to be attached using four bolts. To speed production, a
special machine that simultaneously tightens all four bolts is used. Determine
the largest torque
M
that may be simultaneously applied to each bolt before
the compressor begins to tip.
Problem 5.36
A tractor is fitted with a hole-drilling attachment. The tractor has weight
WVD2000 lb
, the operator has weight
WOD180 lb
, and the supplemental
weights at the front of the tractor weigh WED300 lb.
(a)
Determine the largest thrust that may be produced by the drilling attach-
ment at point A.
(b)
Describe some simple ways the drilling thrust determined in Part (a) can
be increased (e.g., addition of more weight at
E
, removal of weight at
E
,
repositioning of weight from Eto D, and so on).
Solution
Problem 5.37
A spanner wrench is used to apply torque to circular shafts and other similar
shapes. Such wrenches are routinely used in the setup of tools, such as milling
machines, lathes, and so on. The wrench makes contact with the shaft at point
A
, which may be assumed to be frictionless, and at
B
, where a small pin fits into
a hole in the shaft. If
PD80 N
,
LD120 mm
,
rD25 mm
, and
˛D120ı
,
determine the reactions at points Aand B.
Solution
Problem 5.38
In the spanner wrench of Prob. 5.37, determine the range of values for angle
˛
so that the pin at Bwill not slip out of its hole when force Pis applied for
(a) L=r D4.
(b) Any value of L=r.
Solution
672 Solutions Manual
Problem 5.39
An arbor press is used to apply force to the workpiece at point
C
. The length
h
of handle
DE
can be adjusted by sliding it through a hole in shaft
F
such that
50 mm h250 mm
. The press has weight
WD350 N
and simply rests on
the rough surface of a table. Force Pis applied perpendicular to the handle.
(a)
If the handle is horizontal (
˛D0ı
), determine the smallest force
P
that
will cause the press to tip about point A.
(b)
For any possible position of the handle, determine the smallest force
P
and the corresponding value of
˛
that will cause the press to tip about
point A.
Problem 5.40
A portion of a structure is supported by a frictionless V-shaped notch as shown.
Which are the proper support reactions: those shown in Fig. P5.40(b) or those
in Fig. P5.40(c), or are both of these acceptable? Explain.
Problem 5.41
An antenna used for research at a university is shown. It is easily raised and
lowered so that it can be outfitted with different equipment. The antenna is
pinned to a supporting frame at point
A
, and it is raised and lowered using the
gear at
B
to which a hand crank is attached. The antenna and its attached sector
gear weigh
300
and
120 lb
, respectively, and the
100 lb
horizontal force at point
C
models the effect of wind loads during a storm. If the gear at
B
is locked so
it does not rotate, determine the gear tooth force and the reactions at A.
Problem 5.42
Frame
ABCD
is rigidly attached to a gear
E
, which engages two parallel
geared tracks
F
and
G
that are fixed in space. The gear has
4in.
pitch radius.
If the gear has weight
WD8lb
and
PD10 lb
, determine the tooth forces
between gear Eand each track. Hint: A normal force is present at either For
G, but not both.
Problem 5.43
The gear shown slides in a frictionless vertical slot. The gear weighs
WGD
300
N with center of gravity at point
A
. A chain with negligible weight is
wrapped around the gear, and member
BC
, which has negligible weight, is
bolted to the gear.
(a)
If
WD50
N, determine the forces supported by the chain and the
reactions at the bearing Aof the gear.
(b)
Determine the value
W
(where
W > 0
) when the chain is no longer in
tension throughout its entire length.
Problem 5.44
The main sprocket, chain, and pedals of a bicycle are shown. If
PAD400
N,
PCD30
N, and
TbD60
N, determine the tensile force in the top portion of
the chain and the reactions at the bearing
B
of the sprocket. Assume all forces
shown lie in the same plane. Hint: It may be helpful to use the vector approach
to evaluate the moments of some of the forces.
Solution
Tt
Tb
The FBD is shown at the right. To determine the chain tension
Tt
, we
will sum moments about point
B
, and we will use a combination of
the vector approach and scalar approach to evaluate the moments in
this expression.
ErBA D200 mm .cos 50ıO{Csin 50ıO|/; (1)
ErBC D200 mm .cos 50ıO{sin 50ıO|/; (2)
E
PAD400 N.sin 7ıO{cos 7ıO|/; (3)
E
PCD30 N.sin 15ıO{cos 15ıO|/; (4)
XE
MBDE
0W ErBA E
PAC ErBC E
PCTt.80 mm/O
k
CTb.80 mm/O
kDE
0: (5)
In writing Eq. (5), we have used the scalar approach to determine the moments from the chain forces.
Equation (5) becomes
ˇˇˇˇˇˇ
O{O|O
k
cos 50ısin 50ı0
sin 7ıcos 7ı0ˇˇˇˇˇˇ
.200 mm/.400 N/Cˇˇˇˇˇˇ
O{O|O
k
cos 50ısin 50ı0
sin 15ıcos 15ı0ˇˇˇˇˇˇ
.200 mm/.30 N/
Tt.80 mm/O
kCTb.80 mm/O
kDE
0: (6)
After evaluation, the xand ycomponents of Eq. (6) are zero, and with TbD60 N, the ´component is
Tt.80 mm/C60,773 Nmm D0)TtD759:7 N. (7)
Writing the remaining equilibrium equations provides
XFxD0W PAsin 7ıCPCsin 15ıCTtcos 2ıCTbcos 10ıCBxD0)BxD 777:3 N,
(8)
XFyD0W PAcos 7ıPCcos 15ıCTtsin 2ıCTbsin 10ıCByD0)ByD389:1 N.
(9)
Statics 2e 679
Problem 5.45
Frame
BCD
is rigidly attached to a gear
A
, which engages a geared track
E
that is fixed in space. The gear has
30 mm
pitch radius, and portions
BC
and
CD
of the frame are perpendicular. If the gear has weight
WD6N
and
PD4N
, determine the value of
Q
needed so that angle
D30ı
, and also
determine the reactions (tooth forces) between the gear and track.
Problem 5.46
In the frame and gear of Prob. 5.45, if
WD6
N,
PD4
N, and
QD8
N,
determine the value of
when the assembly is in static equilibrium and the
reactions (tooth forces) between the gear and track.
Problem 5.47
Derive Eq. (5.12) on p. 298.
Solution
Problem 5.48
All pulleys are frictionless. Determine the reactions at point
A
and the force
supported by the cable.
Solution
Problem 5.49
All pulleys are frictionless. Determine the reactions at point
A
and the force
supported by the cable.
Problem 5.50
All pulleys are frictionless. Determine the reactions at point
A
and the force
supported by the cable.