Respostas Problemas Cap.1

Prévia do material em texto

MECAˆNICA FUNDAMENTAL – 2013/2 – DF-ICEx
FIS031 – Turma: B2
Respostas de problemas do Cap. 1 da Apostila
Obs: Soluc¸a˜o do problema 1.21 corrigida
1.1 (a)~ı + 2~ − ~k , √6
(b)~ı + ~k ,
√
2
(c) 1
(d) −~ı +~ + ~k , √3
1.3 arccos
√
2/3 = 35◦15′
1.4 (a) −~ıω senωt+~ω coswt, ω
(b) 2~ + 6t~k ,
√
4 + 36t2
(c) cosωt−ωt senωt+ωt2 cosωt+ 2t senωt, (3t2 senωt+ t3ω cosωt)~ı −
(3t2 cosωt− t3ω senωt)~ + ((2t− tω) cosωt− (1 + t2ω) senωt)~k
1.5 (−1±√17)/4
1.10 (1/2)~ı ′ +~ ′ + (
√
3/2)~k ′
1.12  cosφ cos θ cosφ sin θ − sinφ− sin θ cos θ 0
sinφ cos θ sinφ sin θ cosφ

1.14 ~k , ~ − ~k ,~ı − ~k
1.15 ωb
√
1 + 3cos2ωt
1.16 arccos
√
−3/5 = 126◦.87
1.19
√
b2ω2 + 4c2t2,
√
b2ω4 + 4c2
1.21
√
b2ω2(b2ω4+4c2+4c2t2ω2)
b2ω2+4c2t2
, 4c
2t√
b2ω2+4c2t2
1.25 (~av − ~vv˙)/|~a× ~v|
1.26 ~a = −(bω21+bω22 sen2 ω1t)~er+(2bω1ω2 cosω1t)~eφ−(bω22 senω1t cosω1t) ~eθ,
~a(θ = 0) = −bω21~er + 2bω1ω2~eφ