lista2 dinamica II - 2012 respostas

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Gabarito da Lista 2
Thiago Ritto
(tritto@mecanica.ufrj.br)
Carlos Eduardo Ribeiro
(cegribeiro@poli.ufrj.br)
1. •
RV ∗2 =
6lcos2(β)RV ∗1
l + 3lcos2(β)
−R V ∗1
•
ω2 =
6cos(β)RV ∗1
l + 3lcos2(β)
•
HB/∗ =
6cos(β)RV ∗1 ml
2
12l + 36lcos2(β)
2.  F1 − 15ρr2pi�gF2
F3
 =
 21515ρr3pi�(θ˙2cos(θ)− θ¨sen(θ))2
1515ρr
3pi�(θ˙2sen(θ)− θ¨cos(θ))
0

 M1cos(φ)−M2sen(φ)M1sen(φ) +M2cos(φ)
M3 + 2ρr
3pi�gsen(θ)
 =
 00
(115, 5ρr3pi�)α

3. •
H1 =
51
4
mr2Ω
H2 =
27
4
mr2ω
H3 = 0
•
K =
27
8
mr2ω2 +
1
8
mr2ω2
4. •
H1 =
51
4
mr2Ω− 25
4
mΩr2
H2 =
27
4
mr2ω +
5
2
mvr
H3 =
5
2
mΩrx
1
•
K =
27
8
mr2ω2 +
1
2
mv2 +
1
8
mr2ω2
5.
v =
√
2r2[(M +m)gh−K(2∆xh+ 2h2)
(M +m)r2 +mK∗
2