PROBLEM 10.75
Angle
θ
is equal to 45° after a block of mass
m
is hung from member
AB
as shown. Neglecting the mass of
AB
and knowing that the spring is
unstretched when
20 ,
θ
=
°
determine the value of
m
and state whether
the equilibrium is stable, unstable, or neutral.
SOLUTION
Potential Energy
Have
2
1
2
SP
B
V
kx
mgy
=
+
where
(
)
0
0
,
100 mm,
20
rad
9
SP
x
r
r
π
θ
θ
θ
=
−
=
=
° =
cos
,
450 mm
θ
=
=
B
AB
AB
y
L
L
Then
(
)
2
2
0
1
cos
2
θ
θ
θ
=
−
+
AB
V
kr
mgL
and
(
)
2
0
sin
θ
θ
θ
θ
=
−
−
AB
dV
kr
mgL
d
2
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 Spring '08
 Jenkins
 Statics, Energy, Force, Kinetic Energy, Mass, Kilogram, mgLAB cos

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