MAE 101: Homework 4 Solution
October 11, 2011
Problem 10.
(Problem
3.11
from Gross et al). A uniform pole (length
l
, weight
G
) leans against a corner as
shown in the ﬁgure. A rope
S
prevents the pole from sliding. All surfaces are smooth. Determine
the force
S
in the rope.
Solution:
The FBD is shown in the following ﬁgure. Because friction is negligible, all the contact forces will be perpendicular
to the contact plane.
Note that the contact force
N
1
and
N
2
must intersect at point
O
. The distance
OA
can be calculated as
OA
=
h/
sin
α/
sin
α
=
h
sin
2
α
1
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View Full DocumentTake the moment about point
O
we have
X
M
O
=
S
×
h
sin
2
α

G
×
l
2
cos
α
= 0
Solving for
S
, we have
S
=
Gl
2
h
sin
2
α
cos
α
.
Problem 11.
(Problem
3.13
from Gross et al). Two smooth rollers (each having weight
G
and radius
r
) are connected by a rope
(length
a
) as shown in the ﬁgure. A lever (length
l
) subjected to a vertical force
F
exerts contact forces on the rollers.
Determine the contact forces between the rollers and the horizontal plane.
Answer
N
1
=
G

F
l
a
r
1

4(
r
a
)
2
,
N
2
=
G
+
F
l
a
r
1

4(
r
a
)
2
where
N
1
and
N
2
are the contact forces acting on the left and on the right roller, respectively.
Solution:
Assume the angle between the lever and the cable to be
α
, and from geometry we have sin
α
=
a
2
r
and cos
α
=
q
1

(
2
a
r
)
2
. Let’s ﬁrst analyze the lever. The FBD of the lever is drawn as below. The lever has contact forces from
the rollers which are perpendicular to it and also contact force
F
0
from the ground and a load
F
, as shown.
Consider the force equilibrium along the lever we must have
F
sin
α
=
F
0
sin
α
, so that we have
F
0
=
F
. Let’s
know consider the FBD of the whole system. Assume contact force between roller A and ground is
N
1
and roller B
is
N
2
. Draw the FBD of the whole system
Let’s calculate the moment about point
A
. The original problem’s plot is not very clear where the left end of the
lever lies, however we don’t have to know that if we consider the two
F
’s from the ground and the load as a couple.
To calculate the moment generated by those two
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 Spring '08
 ORIENT
 Statics, Force, Simple machine, Bedford

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