PROBLEM 10.71
Two uniform rods AB and CD, of the same length l, are attached
to gears as shown. Knowing that rod AB weighs 3 lb and that rod
CD weighs 2 lb, determine the positions of equilibrium of the
system and state in each case whether the equilibrium is stable,
unstable, or neutral.
PROBLEM 10.71 (Continued)
PROBLEM 10.72
Two uniform rods, each of mass m and length l, are attached to drums that are
connected by a belt as shown. Assuming that no slipping occurs between the
belt and the drums, determine the positions of equilibrium of the system and
state in each case whether the equilibrium is stable, unstable, or neutral.
PROBLEM 10.73
Using the method of Section 10.8, solve Problem 10.39.
Determine whether the equilibrium is stable, unstable, or neutral.
(Hint: The potential energy corresponding to the couple exerted
by a torsion spring is
2
1
2
,
K
where K is the torsional spring
constant and
is the angle of twist.)
PROBLEM 10.39
The lever AB is attached to the horizontal shaft
BC that passes through a bearing and is welded to a fixed support
at C. The torsional spring constant of the shaft BC is K; that is, a
couple of magnitude K is required to rotate end B through 1 rad.
Knowing that the shaft is untwisted when AB is horizontal,
determine the value of
corresponding to the position of
equilibrium when P 100 N, l 250 mm, and
12.5 N m/rad.K
PROBLEM 10.74
In Problem 10.40, determine whether each of the positions of
equilibrium is stable, unstable, or neutral. (See hint for Problem 10.73.)
PROBLEM 10.40
Solve Problem 10.39 assuming that
350 N,P
250 mm,l
and
12.5 N m/rad.K
Obtain answers in each of the
following quadrants:
0 90°, 270° 360°, 360° 450°.
PROBLEM 10.75
A load
W
of magnitude 100 lb is applied to the mechanism at
C
.
Knowing that the spring is unstretched when
15 ,
determine that
value of
corresponding to equilibrium and check that the
equilibrium is stable.
PROBLEM 10.76
A load W of magnitude 100 lb is applied to the mechanism at C.
Knowing that the spring is unstretched when 30 ,
determine that
value of
corresponding to equilibrium and check that the
equilibrium is stable.
PROBLEM 10.77
A slender rod
AB
, of weight
W
, is attached to two blocks
A
and
B
that can move freely in the guides shown.
Knowing that the spring is unstretched when
0,
y
determine the value of
y
corresponding to equilibrium
when
80 N,W500 mm,l
and
600 N/m.k
PROBLEM 10.78
A slender rod AB, of weight W, is attached to two blocks
A and B that can move freely in the guides shown.
Knowing that both springs are unstretched when
0,
y
determine the value of y corresponding to equilibrium
when
80 N,W
l 550 mm, and
600 N/m.k
PROBLEM 10.79
A slender rod
AB
, of weight
W
, is attached to two blocks
A
and
B
that
can move freely in the guides shown. The constant of the spring is
k
,
and the spring is unstretched when
AB
is horizontal. Neglecting the
weight of the blocks, derive an equation in
,
W
,
l
, and
k
that must be
satisfied when the rod is in equilibrium.