Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
Problem 4.10
Repeat Prob. 4.9 if the moment at point Bmay not exceed 5000 in.lb.
Solution
Problem 4.11
The port hull of a catamaran (top view shown) has cleats at points
A
,
B
, and
C
.
A rope having
100 N
force is to be attached to one of these cleats. If the force
is to produce the largest possible counterclockwise moment about point
O
,
determine the cleat to which the rope should be attached and the direction the
rope should be pulled (measured positive counterclockwise from the positive
x
direction). Also, determine the value of
MO
produced. Assume all cleats, point
O, and the rope lie in the same plane.
Problem 4.12
Frame
ABC
has a frictionless pulley at
C
around which a cable is wrapped.
Determine the resultant moment about point
A
produced by the cable forces if
WD5kN and
(a) ˛D0ı.
(b) ˛D90ı.
(c) ˛D30ı.
Solution
Problem 4.13
Frame
ABC
has a frictionless pulley at
C
around which a cable is wrapped. If
the resultant moment about point
A
produced by the cable forces is not to exceed
20 kNm
, determine the largest weight
W
that may be supported and the value
of
˛
for which the moment about
A
is the largest. Note that the value of
W
you
determine must not produce a moment about
A
that exceeds
20 kNm
for any
possible value of ˛.
Problem 4.14
The load-carrying capacity of the frame of Prob. 4.13 can be increased by
placing a counterweight
Q
at point
D
as shown. The resultant moment about
point Adue to the cable forces and Qis not to exceed 20 kNm.
(a)
Determine the largest value of counterweight
Q
.Hint: Let
WD0
and
determine Qso that MAD20 kNm.
(b)
With the value of
Q
determined in Part (a), determine the largest weight
W
that may be supported and the corresponding value of
˛
. Note that
the value of
W
you determine must not produce a moment about
A
that
exceeds 20 kNm for any possible value of ˛.
Problem 4.15
A bolt whose shank lies on the
y
axis is to be loosened. In Fig. P4.15(a), an
open-end wrench is used where the handle lies along the
x
axis. In Fig. P4.15(b),
a ratchet wrench is used where the handle is parallel to the
x
axis. If the force
applied to the handle of the wrench acts in the
´
direction, determine the
moment of this force about point
O
for each wrench. Speculate on which of
the wrenches will be more effective in loosening the bolt. Explain.
Problem 4.16
Repeat Prob. 4.15 if the force applied to the handle of the wrench has direction
angles xD72ı,yD60ı, and ´D144ı.
Problem 4.17
A flat rectangular plate is subjected to the forces shown, where all forces are
parallel to the
x
or
y
axis. If
FD200 N
and
PD300 N
, determine the
resultant moment of all forces about the
(a) ´axis.
(b) aaxis, which is parallel to the ´axis.
Problem 4.18
A flat rectangular plate is subjected to the forces shown, where all forces are
parallel to the
x
or
y
axis. If
PD300 N
, determine
F
when the resultant
moment of all forces about the ´axis is M´D 100 Nm.
Problem 4.19
Repeat Prob. 4.18 if the resultant moment of all forces about the
a
axis is
MaD 100 Nm.
Problem 4.20
The structure shown supports a force
FD20 kN
. Use the vector approach with
the position vectors cited below to determine the moment of the force about
point A.
(a) Use the position vector from point Ato point D, namely ErAD .
(b) Use the position vector from point Ato point E, namely ErAE .
Problem 4.21
The aircraft shown has three engines (the engine on the right-hand wing is
hidden in the figure). During a test, the right-hand engine is shut down. If
the thrust produced by engines
A
and
B
are
E
FAD30;000 O{lb
and
E
FBD
.29;700 O{C4000 O
k/ lb
, and points
A
and
B
lie on the lines of action of
E
FA
and
E
FB
, respectively, with coordinates
A.6; 25; 7/ ft
and
B.80; 0; 20/ ft
,
determine the resultant moment of the two engine thrusts about the origin of
the coordinate system, point O.
Problem 4.22
Structure
OBCD
is built in at point
O
and supports a 50 lb cable force at point
C
and 100 and 200 lb vertical forces at points
B
and
D
, respectively. Using a
vector approach, determine the moment of these forces about
(a) point B.
(b) point O.
Solution
Problem 4.23
Repeat Prob. 4.22, using a scalar approach.
Solution
Problem 4.24
Structure
OAB
is built in at point
O
and supports forces from two cables.
Cable
CAD
passes through a frictionless ring at point
A
, and cable
DBE
passes through a frictionless ring at point
B
. If the force in cable
CAD
is 250 N
and the force in cable DBE is 100 N, use a vector approach to determine
(a) the moment of all cable forces about point A.
(b) the moment of all cable forces about point O.
Problem 4.25
Repeat Prob. 4.24, using a scalar approach.
Problem 4.26
Structure
OABC
is built in at point
O
and supports forces from two cables.
Cable
EAD
passes through a frictionless ring at point
A
, and cable
OC G
passes through a frictionless ring at point
C
. If the force in cable
EAD
is
800 lb and the force in cable OC G is 400 lb, determine
(a) the moment of forces from cable OC G about point B.
(b) the moment of all cable forces about point A.
(c) the moment of all cable forces about point O.
Problem 4.27
Repeat Prob. 4.26, using a scalar approach.
