Download Problem 2 - Purdue College of Engineering

Problem 8.154
A
B
30o
M0
C
D
Two uniform rods each of weight W
and length L are maintained in the
position shown by a couple M0
applied to rod CD. Knowing that the
coefficient of static friction between
the rods is 0.40, determine the
range of values of M0 for which
equilibrium is maintained.
Problem 8.154
A
B
30o
M0
C
D
Solving Problems on Your Own
Two uniform rods each of weight W
and length L are maintained in the
position shown by a couple M0
applied to rod CD. Knowing that the
coefficient of static friction between
the rods is 0.40, determine the
range of values of M0 for which
equilibrium is maintained.
When the motion is impending and ms is known; you must find
some unknown quantities, such as a distance, an angle, the
magnitude of a force, or the direction of a force.
a. Assume a possible motion of the body and, on the free-body
diagram, draw the friction force in a direction opposite to that
of the assumed motion.
Problem 8.154
A
B
30o
M0
C
D
Solving Problems on Your Own
Two uniform rods each of weight W
and length L are maintained in the
position shown by a couple M0
applied to rod CD. Knowing that the
coefficient of static friction between
the rods is 0.40, determine the
range of values of M0 for which
equilibrium is maintained.
b. Since motion is impending, F = Fm = msN. Substituting for ms
its known value, you can express F in terms of N on the freebody diagram, thus eliminating one unknown.
c. Write and solve the equilibrium equations for the unknowns.
Problem 8.154 Solution
Assume a possible motion of the body and,on the free-body
diagram, draw the friction force in a direction opposite to that
of the assumed motion.
Impending Motion: Assumed clockwise
Free-Body Diagrams
L
W
2
Ax
Ay
B
A
N F
N
L cos q
D
(L /2)cos q
F
W
L sin q
Cx
C
M0
Cy
Problem 8.154 Solution
Assume a possible motion of the body and,on the free-body
diagram, draw the friction force in a direction opposite to that
of the assumed motion.
Impending Motion: Assumed clockwise
Free-Body Diagrams
L
W
2
Ax
Ay
B
A
N F = ms N
N
L cos q
D
(L /2)cos q
W
F = ms N
L sin q
M0
Cx
C
Cy
Since motion is impending,
F = Fm = msN. Substituting
for ms its known value, you
can express F in terms of
N on the free-body
diagram, thus eliminating
one unknown.
Problem 8.154 Solution
Write and solve the equilibrium equations for the unknown.
Ax
A
W
L
2
B
F = ms N
Ay
L cos q
+
N
S MA = 0:
N (Lcos q) - W (L/2) = 0
W
N =
2 cos q
ms W
F = ms N = 2 cos q
Problem 8.154 Solution
N
(L /2)cos q
D
F = ms N
W
Write and solve the equilibrium
equations for the unknown.
W
N =
2 cos q
L sin q
M0
Cx
C
Cy
ms W
F = ms N = 2 cos q
+ S MC = 0: M0 - N (Lcos q) + F (Lsin q) - W (L/2)(cos q) = 0
ms W
W
M0 (Lcos q) +
(Lsin q) - W (L/2)(cos q) = 0
2 cos q
2 cos q
1
M0 = 2 WL (cos q + 1 - ms tan q )
= (0.5)WL (cos 30o + 1 - 0.40 tan 30o)
M0 = 0.818WL
Problem 8.154 Solution
M0 = 0.818WL
For Impending Counterclockwise Motion of the rods, we change
the sign of ms. Therefore, M0 is
1
M0 = 2 WL (cos q + 1 + ms tan q )
= (0.5)WL (cos 30o + 1+ 0.40 tan 30o)
M0 = 1.0484 WL
N
D
(L /2)cos q
F = ms N
Range of M0 for Equilibrium:
W
L sin q
M0
Cx
C
Cy
0.818WL < M0 < 1.048WL