:
1. 
m1 = 1 m2 = 2 v1 = 10 / v2 = 15 / . . ?
:
m1 = 1 , m1 m2 -
m2 = 2 -
v1 = 10 / :
v2 = 15 / 
, (1)
v´1 = 0 v .
_________ x y,
Q -? :
OX) m1v1 = m2vx (2)
OY) m2v2 = m2vy, (3)
vx vy 
.
:
; 
(4,5)
, - :
(6)
: 25 .
2. , , a =30, 0,3.
:
a =30 II , :
μ = 0,3 1. , :
_______ 
- ;
-? 
- ;
- .
2. II :
3. , . x , y .
OX) mg sin α - F = m (1)
OY) mg cos α + N = 0 (2)
, F = μN (3)
(1) (2) (3):
mg sin α − μN = m
mg cos α = N
, :
mg sin α − μmg cos α = m
: α = sin α − μ cos α
α = 0,24 /2.
: α = 0,24 /2.
3. 0,5 50 : 1) ; 2) , , 20 ; 3) .
:
m = 0,5 :
R = 0,5 I = mR2/2
a2 = 0,2 I = 0,5(0,5)2/2 = 0,0625 2.
a3 = 0,5 :
_______ I = I + ma2,
-? I − , ( 1),
a − .
I = 0,0625 + (0,5(0,2)2) = 0,0825 2.
, a3 = 0,5 :
|
|
|
I = 0,0625 + (0,5(0,5)2) = 0,1875 2.
: I1 = 0,0625 2, I2 = 0,0825 2, I3 = 0,1875 2.
: .
4. 200 , 40 /. 80 . , ? .
:
m = 200
ν1 = 0,67 -1 : L1 = L2
m = 80 L1 = mR2/2 (2π ν1)2
_______ L2 = (mR2/2 + m R2) (2π ν2)2
ν2 -? I = mR2/2 − , I = m R2 − .
ν2, :
_____________ _____________
m (ν1)2 200 (0,67)2
ν2 = √ −−−−−−−−−−−− = √ −−−−−−−−−−−−
| m + 2m | 200 + 280
: ν2 ≈ 0, 5 -1.
:
1. 0,3 , , . .
:
r = 310-4 -:
θ = 0 h = (2α cos θ)/ ρgr
ρ = 103 /3 cos θ = 1. -
α = 72 / : h = 2α/ ρgr.
_______ h = (27210-3)/ 103 9,8 310-4 ≈ 5 .
h -? : h = 5 .
2. , . , 2 ? ( 7,4×10-2 /, 103 /3, ).
:
h = 210-2 -:
θ = 0 h = (2α cos θ)/ ρgr
ρ = 103 /3 cos θ = 1. -
α = 7,4×10-2 / :
_______ h = 2α/ ρgr.
r -? : r = 2 α/ ρgh.
r = (27,410-2)/ 103 10 210-2 = 7,410-4 = 0,74 .
: r = 0,74 .
3. , 1 2 1 8×10-8 . 0,04 2/.
:
Δs = 12 :
Δt = 1 c m = − D(Δρ/Δx)ΔsΔt
m = 810-8 : Δρ/Δx = m/ DΔsΔt
D = 0,04 2/ Δρ/Δx = 810-8/0,0411 = 210-2 /4
_______
Δρ/Δx -? : Δρ/Δx = 0,02 /4.
4. 6 , 1030 /3, 6 ? 900 /3. 1,810-3 .
:
|
|
|
ρ = 1030 /3 ,
ρ = 900 /3 : ( ), (-
t = 21600 ), ( ). -
η = 1,810-3 ( ).
_____________ ,
s -? , ( -, ):
Y) F − mg − F = 0
:
m = ρV
:
V = 4πr3/3
, :
mg = ρg4πr3/3
( ):
F = mg = ρg4πr3/3
:
F = 6πη rv
:
6πη rv = ρg4πr3/3 − ρg4πr3/3
, :
s = vt
6πη r s/ t = g4πr3 (ρ − ρ)/3
s:
s = (2gr2t (ρ − ρ) /9η)
s = (29,8910-1221600 (1030 − 900) /91,810-3) ≈ 0,03 = 3 .
: s = 3 .
: .
5. 137. (84,87×10-22 )
:
= 410
:
_____________ = ikT/2,
-? i − .
3:
i = n = 3
k = 1,3810-23 / − .
= 31,3810-23410/2 = 848,710-23 = 84,87×10-22 .
: = 84,87×10-22 .
