Problem 7.124
Bars
AB
and
BC
are uniform with masses
mAB D2kg
and
mBC D1kg
, respectively. Their lengths are
LD1:25
m and
HD0:75
m. Bar
BC
is pin-connected to a fixed support at
C
that is a distance
ıD0:2
m from the ground. Bar
AB
is pin-
connected at
A
to a uniform wheel with radius
RD0:60
m and
mass
mOA D5kg
. Note that
A
is at a distance
from the center
of the wheel. At the instant shown,
A
is vertically aligned with
O
; in addition,
AB
and
BC
are parallel and perpendicular to the
ground, respectively. At this instant, bar
BC
is rotating clockwise
with an angular velocity of
2rad=s
and an angular acceleration of
1:2 rad=s2
. Assuming that the wheel rolls without slip, determine
the force
P
that is applied to the wheel at the instant shown. In addi-
tion, determine the minimum static coefficient of friction necessary
for the wheel not to slip.
Solution
The FBDs of each of the three rigid bodies are shown at the right.
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Dynamics 2e 1667
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Computation.
Substituting the expressions for the mass moments of inertia,
aDx
and
aDy
from Eq. (14),
˛OA
and
˛AB
from Eq. (13),
aEx
and
aEy
from Eq. (11), and
aOx D R˛OA
and
aOy D0
into the nine
Newton-Euler equations given by Eqs. (1)–(9),
Solving this system of equations, we obtain the following system of nine equations in the nine unknowns:
F,N,Cx,Cy,Ax,Ay,Bx,By, and P:
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Dynamics 2e 1669
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Problem 7.125
Two identical uniform bars are pinned together at one end, and each
bar has a roller at its other end. The rollers can roll freely along the
horizontal surface as shown. Each bar has mass
m
and length
L
, and
a horizontal force
P
is applied to bar
BC
at
B
. Although the bars
can rotate relative to each other, for a given value of
P
there exists a
corresponding value of such that the system moves with constant.
(a)
Find the forces on the bars at
A
and
B
and show that they are
independent of P.
(b)
Determine
as a function of
P
and find
0
as
P!0
and
1
as
P! 1.
Neglect the mass of the rollers and any friction in their bearings.
Solution
Part (a)
where ˛BC is the angular acceleration of bar BC and its mass moment of inertia is IDD1
12 mL2.
Force Laws. All forces have been accounted for on the FBD.
Kinematic Equations.
Since thw angle
is constant, that implies that both bars are in pure translation.
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1671
Computation.
Substituting the expressions for the mass moments of inertia and the kinematic equations
into the six Newton-Euler equations, we obtain the following system of six equations in the six unknowns
a
,
Ay,By,Cx,Cy,:
Part (b)
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