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12.64. Model:
Model the beam as a rigid body. For the beam not to fall over, it must be both in translational
equilibrium
net
(0
N
)
F
=
G
G
and rotational equilibrium
net
N
m
)
.
τ
=
Visualize:
The boy walks along the beam a distance
x
, measured from the left end of the beam. There are four forces acting
on the beam.
1
F
and
2
F
are from the two supports,
( )
G
b
F
G
is the gravitational force on the beam, and
()
G
B
F
G
is
the gravitational force on the boy.
Solve:
We pick our pivot point on the left end through the first support. The equation for rotational equilibrium
is
Gb
2
GB
(
) (2.5 m)
(3.0 m)
(
)
0 N m
FF
F
x
−+
−
=
22
2
(40 kg)(9.80 m/s )(2.5 m)
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 Fall '09
 geller

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