Чертов А.Г. Решебник
Подождите немного. Документ загружается.
m
1
v
2
1
+ m
2
v
2
2
= m
1
u
2
1
+ m
2
h
m
1
m
2
(v
1
+ u
1
) − v
2
i
2
1 · 4
2
+ 2 · 3
2
= 1 · u
2
1
+ 2 ·
h
1
2
(4 + u
1
) − 3
i
2
; 34 = u
2
1
+ 2 ·
h
1
2
· u
1
− 1
i
2
u
1
3
2
u
2
1
− 2u
1
− 32 = 0; u
2
1
−
4
3
u
1
−
64
3
= 0;
u
1
=
2
3
±
s
2
3
2
+
64
3
=
2
3
±
14
3
u
1
, u
2
v
1
, v
2
u
1
=
2
3
+
14
3
=
16
3
= 5, 33
/ ; u
2
=
1
2
(4 +
16
3
) − 3 =
5
3
= 1, 66
/ .
m
1
= 3 ; v
1
= 2 /
m
2
= 5 .
A
-
m
1
v
1
m
2
-
u
m
1
+ m
2
u
m
1
v
1
= (m
1
+ m
2
)u; u =
m
1
v
1
m
1
+ m
2
.
T
1
=
m
1
v
2
1
2
T
2
=
(m
1
+ m
2
)u
2
2
=
(m
1
+ m
2
)
2
·
m
2
1
v
2
1
(m
1
+ m
2
)
2
=
m
2
1
v
2
1
2(m
1
+ m
2
)
.
A = T
1
− T
2
=
m
1
v
2
1
2
−
m
2
1
v
2
1
2(m
1
+ m
2
)
=
m
1
v
2
1
2
·
1 −
m
1
m
1
+ m
2
=
m
1
v
2
1
2
·
m
2
m
1
+ m
2
;
A =
3 · 2
2
2
·
5
3 + 5
= 3, 75
.
m
1
= 0, 5 = 500 ; m
2
=
120
.
η
A
A
?
m
1
u
1
m
2
u
2
u
1
m
1
u
1
= (m
1
+ m
2
)u
2
T
1
=
m
1
u
2
1
2
T
2
=
(m
1
+ m
2
)u
2
2
2
;
u
2
=
m
1
u
1
m
1
+ m
2
;
T
2
=
(m
1
+ m
2
)
2
·
(m
1
u
1
)
2
(m
1
+ m
2
)
2
=
m
2
1
u
2
1
2(m
1
+ m
2
)
.
η =
T
2
T
1
=
m
2
1
u
2
1
2(m
1
+ m
2
)
·
2
m
1
u
2
1
=
m
1
m
1
+ m
2
; η =
500
500 + 120
= 0, 81.
m
1
= 4 ; v
1
= 5 / ;
m
2
= 6 ; v
2
= 2 / .
u
1
, u
2
-
m
1
v
1
v
2
m
2
-
u
1
u
2
m
1
v
1
− m
2
v
2
= −m
1
u
1
+ m
2
u
2
(1)
m
1
v
2
1
2
+
m
2
v
2
2
2
=
m
1
u
2
1
2
+
m
2
u
2
2
2
(2)
u
2
u
2
=
m
1
m
2
(v
1
+ u
1
) − v
2
m
1
v
2
1
+ m
2
v
2
2
= m
1
u
2
1
+ m
2
h
m
1
m
2
(v
1
+ u
1
) − v
2
i
2
4 · 5
2
+ 6 · 2
2
= 4 · u
2
1
+ 6 ·
h
4
6
(5 + u
1
) − 2
i
2
124 = 4 · u
2
1
+ 6 ·
h
4
3
+
2
3
· u
1
i
2
u
1
u
2
1
+ 1, 6u
1
− 17 = 0
u
1
= −0, 8 ±
q
(0, 8)
2
+ 17 = −0, 8 ± 4, 2;
u
1
= −0, 8 − 4, 2 = −5 /
u
1
= −0, 8 + 4, 2 = 3, 4 / ; u
2
=
4
6
(5 + 3, 4) − 2 = 3, 6
/
m = 35 ; v = 0, 2 / ;
∆l = 12 .
F
max
, ∆t
L
L
L
B
B
B
m
m m
v
=
k∆l
2
2
=
mv
2
2
k
k =
mv
2
∆l
2
=
35 · 10
3
· (0, 2)
2
(0, 12)
2
= 9, 72 · 10
4
.
F
max
= k · ∆l = 9, 72 · 10
4
· 0, 12 = 1, 17 · 10
3
.
∆t =
T
4
=
2π
4
r
m
k
=
π
2
r
m
k
;
∆t =
3, 14
2
s
35 · 10
3
9, 72 · 10
4
= 0, 94
.
m
1
= 5 ; v
1
= 1 /
m
2
= 2 ; v
2
= 0
u
1
, u
2
-
m
1
v
1
m
2
-
-
u
1
u
2
m
1
v
1
= m
1
u
1
+ m
2
u
2
(1)
m
1
v
2
1
2
=
m
1
u
2
1
2
+
m
2
u
2
2
2
(2)
u
2
u
2
=
m
1
m
2
(v
1
− u
1
)
m
1
v
2
1
= m
1
u
2
1
+ m
2
m
1
m
2
2
(v
1
− u
1
)
2
v
2
1
= u
2
1
+
m
1
m
2
(v
1
− u
1
)
2
= u
2
1
+
m
1
m
2
v
2
1
− 2
m
1
m
2
v
1
u
1
+
m
1
m
2
u
2
1
u
1
1 +
m
1
m
2
u
2
1
− 2
m
1
m
2
v
1
u
1
+
m
1
m
2
− 1
v
2
1
= 0
1 +
5
2
u
2
1
− 2 ·
5
2
· 1 · u
1
+
5
2
− 1
· 1
2
= 0; u
2
1
−
10
7
· u
1
+
3
7
= 0
u
1
=
5
7
±
s
5
7
2
−
3
7
=
5
7
±
2
7
u
1
=
5
7
+
2
7
= 1
/
u
1
=
5
7
−
2
7
=
3
7
= 0, 43
/ ;
u
2
=
5
2
(1 − 0, 43) = 1, 42
/ .
k
1
= 400 / ; k
2
= 250 / ;
∆l
1
= 2 = 0, 02 .
A
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
-
k
1
k
2
F
F = k∆l
∆l
k
1
∆l
1
= k
2
∆l
2
; l
2
=
k
1
k
2
· ∆l
1
.
=
k∆l
2
2
,
=
k
1
∆l
2
1
2
+
k
2
∆l
2
2
2
=
k
1
∆l
2
1
2
+
k
2
2
·
k
2
1
k
2
2
∆l
2
1
=
=
k
1
∆l
2
1
2
·
1 +
k
1
k
2
!
.
A = =
400 · (0, 02)
2
2
·
1 +
400
250
= 0, 21 .
m
1
= 10 ; v = 300 / ;
m
2
= 200
; k = 25 / .
x
A
A
A
A
A
A
~u
m
2
-
k
~v
m
1
u
m
1
v − m
2
u = 0; u =
m
1
m
2
v.
=
kx
2
2
;
kx
2
2
=
m
2
u
2
2
.
x
2
=
m
2
u
2
k
; x =
r
m
2
k
· u x =
r
m
2
k
·
m
1
m
2
v.
x =
s
0, 2
25 · 10
3
·
0, 01
0, 2
· 300 = 0, 042
= 4, 2 .
k = 500 / ; F = 100 ;
∆l = 2 = 0, 02 .
A
A =
2
−
1
,
1 2
A =
kx
2
2
2
−
kx
2
1
2
F = kx
1
x
1
= F/k
x
2
= x
1
+ ∆l =
F
k
+ ∆l
A =
k
2
·
F
k
+ ∆l
2
−
k
2
·
F
k
2
=
=
k∆l
2
·
2F
k
+ ∆l
; A =
500 · 0, 02
2
·
2 · 100
500
+ 0, 02
= 2, 1
.
k
1
= 0, 5 / ; k
2
= 1 / ;
∆l = 4
.
T
T
T
T
T
T
T
T
T
A
A
b
b
b
H
H
k
1
k
2
∆l
=
k∆l
2
2
.
=
k
1
∆l
2
2
+
k
2
∆l
2
2
=
(k
1
+ k
2
)∆l
2
2
=
=
(500 + 1000) · (4 · 10
−2
)
2
2
= 1, 2
.
k = 800 / ; x = 6 ;
∆x = 8 .
A
L
L
L
B
B
B
-
∆x
k
A =
2
−
1
,
1 2
1
=
kx
2
2
;
2
=
k(x + ∆x)
2
2
;
A =
k(x + ∆x)
2
2
−
kx
2
2
=
k[(x + ∆x)
2
− x
2
]
2
;
A =
800 · [(0, 06 + 0, 08)
2
− (0, 06)
2
]
2
= 6, 4
.
∆l = 3 ; h = 8 .
∆l
2
H
H
P
P
P
P
?
6
∆l
Z
Z
"
"
a
a
"
"
X
X
6
?
h
F = mg
F = mg = k · ∆l
m k h
∆l
2
= mg(h + ∆l
2
)
mg(h + ∆l
2
) =
1
2
· k(∆l
2
)
2
mg
∆l(h + ∆l
2
) =
1
2
· (∆l
2
)
2
(∆l
2
)
2
− 2∆l∆l
2
− 2∆lh = 0
(∆l
2
)
2
− 0, 6∆l
2
− 4, 8 = 0
∆l
2
= 0, 3 ±
q
(0, 3)
2
+ 4, 8 = 0, 3 ± 2, 21
.
∆l
2
= 0, 3 + 2, 21 = 2, 51 .
k = 150 / ; m = 8 ;
∆x = 4 .
v
A
A
A
A
A
A
-
k
~v
=
k∆x
2
2
k∆x
2
2
=
mv
2
2
.
v
2
=
k∆x
2
m
; v =
s
k
m
· ∆x; v =
s
150
0, 008
· 0, 04 = 5, 5
.
m = 16 = 1600 ; v = 0, 6 / ;
∆l = 8 = 0, 08 .
k
j j
m
-
v
C
C
C
C
C
C
mv
2
2
=
k(∆l)
2
2
∆l
k =
mv
2
(∆l)
2
=
1600 · (0, 6)
2
(0, 08)
2
= 9 · 10
5
h = 20 .
v
a
a
a
a
a
a
a
a
a
a
a
a
l
l
6
?
h
-
v
m R
mgh
mgh =
mv
2
2
+
Jω
2
2
,
J =
1
2
mR
2
ω v
v = ωR; ω = v/R.
mgh =
mv
2
2
+
1
2
mR
2
·
1
2
·
v
R
2
=
mv
2
2
+
mv
2
4
=
3
4
mv
2
; gh =
3v
2
4
;
v =
s
4
3
gh =
s
4
3
· 9, 8 · 0, 2 = 1, 62
/ .
m = 12 ; D = 30 ;
ϕ = A + Bt + Ct
3
;
A = 4
; B = −2 / ;
C = 0, 2 /
3
; t = 3
.
M
M = J · ε
J ε
R = D/2
J = mR
2
=
mD
2
4
ω =
dϕ
dt
= (A + Bt + Ct
3
)
0
= B + 3Ct
2
;
ε =
dω
dt
= (B + 3Ct
2
)
0
= 6Ct;
M =
mD
2
4
· 6Ct =
3
2
mD
2
Ct
M =
3
2
· 12 · (0, 3)
2
· 0, 2 · 3 = 0, 97
· .
D = 60 ; m = 2 ;
t = 3 ; ω = 9 / .
J
&%
'$
*
R
m
?
mg
?
F
6
F
?
a
mg F
a =
mg − F
m
= g −
F
m
;
M = F R =
F D/2
ε =
M
J
=
F D
2J