≪ R,s<h
vd = 2gR z0 R z0 = 2gR h R + h .
d = √2gh h ≫ R
d = 2gR, 11, 2km
vz = √2
vd z = R
h
gs
v
z t ξ2 = z/z0 t = z z0 √z0z 2gR2(z0 z) dz = 1 R 2z3 0 g √z/z0 1 ξ2 1 ξ2 dξ = 1 R z3 0 2g z z0 1 z z0 +arccos z z0 . ξ2 1 ξ2 dξ = 1 ξ2 1 1 ξ2 dξ = 1 ξ2dξ + dξ 1 ξ2 = ξ 1 ξ2 ξ2 1 ξ2 dξ + dξ 1 ξ2 h z = R t
1
2
√
R
R R
h
π/
t
π 2
2
2 . h
arccos R R
h ≈
h R = h R + O h R 3/2 tR = 2h/g h Fz = 1 2 CSρv2 ρ S C C =0, 03 C =0, 48 C =1, 33
v
· s 1
R =
R R + h
g
Rh +(
+ h)arccos
+ h
≫ R
2
R =
h3
gR
≪ R x √1 x2
+
arcsin
h
mz = mg + Kv2 z
k = K/m> 0
z = g + kv2 z
(¨z< 0 ⇒ kv2 z <g) ξ = k g vz
t = vz 0 dvz g + kv2 z = 1 gk
√k/gvz 0 dξ 1 ξ2 = 1 2 1 gk ln 1+ ξ 1 ξ
vz = g k tgh( gkt),z = t 0 vz dt = h 1 k ln[cosh( gkt)]. k → 0
vz = gt + 1 3 g 2kt3 + O(kt5),z = h 1 2 gt2 + 1 12 g 2kt4 + O(kt6).
g/k k
vz →
v
CSρ m =100kg,C =1, 33, d =6 ρ =1, 276 3 v ≈ 6, 5 1 1 1 1◦ z′ x′ y′
= 2mg
r′ = r R(t) R
a ′ = ag A Ω × (Ω × r ′) Ω × r ′ 2Ω × v ′
=7, 292 10 5 1
= Ω×(Ω×R) S′
r′ dv′ dt = g +2v ′ × Ω
C =2mv′Ωsin φ φ g ≡ (0, 0, g), Ω ≡ (0, Ωcos φ, Ωsin φ)
′ =2y′Ωsin φ 2z′Ωcos φ, y′ = 2x′Ωsin φ, z′ = g +2x′Ωcos φ.
Ω Φ
O
Ω z’ y’
R O x’
’
Ω
Ω
R Ω2
φ′ R φ′ Ω2R
, 4 2 g 6′ 11′ φ S′
x
Ukázka elektronické knihy
A
cos
=3
Ω
F