Giáo trình vật lí đại cương

343
Giaựo Trỡnh Vaọt Lớ ẹaùi Cửụn
g
Taọp 1: Cụ Nhieọt ẹieọn

P S CC BI TP
Chng 1:
1.1: b, d, f. 1.2: PTQ; khụng. 1.3: a) y =
2
x
2
; b)
x
20
y =
; c) y = 2x
2
1;
d) z = 2x +1; e)
1
100
y
25
x
22
=+
; f) (x 5)
2
+ (y 4)
2
= 400. 1.4: 39,4km/h.

1.5: 43,6km/h. 1.6: 62,3 km/h. 1.7:
k
v
v
3
2
s
0
0
=
;
0tb
v
3
2
v =
. 1.8:
;
2
tb
)a
2

2
xb
v)b
tb
=
. 1.9: . 1.10: t
s/m5,11v;s/m10v);6,8,0(v

tb
===

1
= 1s; t
2
= 2s;
t
3
= 3s; s = 0,77m/s. 1.11: a) 1,6cm; 3m ; b) 2s; 2,4cm; 565m. 1.12: a) y= 2x
2
+ x;
b)
; c)
)16,0(a);2,2(v ==

2
nt
s/m28aa ==
; R = 70,7cm; d) t = 0,25s;
e) 0,57m. 1.13:
2
3
23
c
bS4
1ca;
bS2
c
R

+==
. 1.14:
)A1(
B2
a
v
2
o
+=
.
1.15:
k
v
3
v2
s
oo
=
;
3
v
v

0
tb
=
. 1.16: a)
4
x
y
2
=
; b) 45
0
. 1.17: a)
2
x
xy
2
=
; c) t
= 1s d) a
t
= 3,98m/s
2
; a
n
= 0,44 m/s
2
; R = 745m; e) 42m. 1.18: b) t = 1/;

=
2

r
s
0
.
1.19:
= sin2
0
. 1.20:
3
0
tb

=
. 1.21: s = 85m. 1.22: t
1
= 0,894s; t
10
=
0,145s. 1.23: s = At. 1.24: a) = 3,14 rad/s; b) v = 1,02 m/s; a
t
= 1,02 m/s
2
; a
n
= 3,2
m/s
2
; a = 3,36 m/s
2
; c) s = 0,51m. 1.25:

15

=
rad/s
2
; 240 vũng. 1.26: 22m.
1.27:b)70,7s c) 2500m; d) a
t
= 7m/s
2
, a
n
= 7,14m/s
2
, R = 35000m. 1.29:
2
2
2
1
2211
vv
vv
t
+
+
=

;
2
2

2
1
1221
min
vv
|vv|
d
+

=

.
1.30:
m802/ad)b;s25
vu
au
t)a
22
===

=

Chng 2:
2.5:a) f
ms
= àmg; a=
m
F
àg; b)f
ms

= à(mg Fsin);
g
m
)sin(cosF
a à
à+
=

c) F
ms
= à(mg + Fsin);
g
m
)sin(cosF
a à

à
=
.
ẹAP SO CAC BAỉI TAP
344

2.6:
)N(106
)sin(
cosP
T
AC
=
+

=
;
)N(137
)sin(
cosP
T
BC
=
+

=
.
2.8:
1e
1e
.
k
g
v
t.gk2
t.gk2

+
=
AB
AB
mm
mm
ga

+

=
. 2.9:
k
v
s;evv
0
kt
0
==

.
2.10:
21
21
mm
mm
ga
+
à
=
; m
2
khụng b trt khi m
2


à
1

m
. 2.11:
21
12
m4m
mm2
ga
+

=

2.12:
g
m
)sin(cosF)sin(cosF
a
21
à
à+à+
=
. 2.13: F
ht
= mg.tg; F
cd
=
cos
mg
. 2.14:a) a = 1m/s
2
; T

12
= 7,2N; T
23
= 1,8N; t = 2s; b) cú, sau 1s.
2.15: a)
)cos
mm
mm
(singa
21
2211

+
à+à
=
;
21
2121
mm
cosg)(mm
Q
+
àà
=
;
b)
21
2211
min
mm

mm
tg
+
à+à
=
.
2.16: a)
à+

cossin
m
m
1
2
;
21
21
mm
)cos(sinmm
ga
+
à+
=
;
b)sin > àcos v
à

cossin
m
m

1
2
;
21
12
mm
m)cos(sinm
ga
+
à
=
;
c)
à+

cossin
m
m
1
2
, nu sin

àcos
hoc

à+
2
1
m
cossin

m
à cossin
m
1
, nu sin > àcos.
2.17: a)
)
R
v
cosg(mQ
2
=
, ti nh cu. 2.19: 6m/s; 2.20: 2kgm/s; 5m.
2.21:
gv =
. 2.22:
tm
Ft
v
0
à
=
. 2.23:
)
tm
m
ln(uvv
0
0
0

à
+=
.
2.24: L = L
z
= - ẵ mv
o
gt
2
cos; L = - ẵ mv
0
3
cos.sin
2
. 2.25: 2,7.10
40
kgm
2
/s
2.26:
;
tb2M

=
b/at =
; M = 2
ab
. 2.27:
3
4

0
2
0
r
Rm
T

=
;
2
0
0
r
R






=
.
2.28:
. 2.30:

= pxrL'L
0
g)mm)((F
2121max
+à+à=

.
2.31:
1
m
m4
m
m
1
m
m4
m
m
ga
2
1
2
1
0
1
2
1
1
++
+
=
; m
1
i xung khi
20
20

1
m4m
mm
m
+

;
345
Giaựo Trỡnh Vaọt Lớ ẹaùi Cửụn
g
Taọp 1: Cụ Nhieọt ẹieọn

2.32:
à
à+
=
sincos
cossin
ga
max0
. 2.33:

g
min
=
; .
)g(mT
2

=

2.34:
s/m10
gR
v
min
=
à
=
.
3.35: a)
)cos(sing)sin(cosa
2
t
0
à+à+
=

;

Chng 3:
3.1: 2,83kg. 3.2: 982kg. 3.3: 546kg. 3.5: tng m = 3m. 3.6: chn trc Ox, Oy trựng
vi OA, OC thỡ
)
10
a7
,
2
a
(G
. 3.7:

=
3
R4
x
G
;
2
3
R4
x
G

=
. 3.8: a)

=
3
a4
x
G
; b)

=
3
b4
x
G
. 3.9:
8

R3
z
G
=
. 3.10:
22
2
rR
ar
OG

=
;
6
R
OG =
.
3.11:
33
3
rR
ar
OG

=
;
14
R
OG =
. 3.12:

)cb(2
acbc2b
x
2
G
+
++
=
;
4
ab3
x
G
+
=
.
3.13:
2
R
h
. 3.14: xem vớ d 2. 3.15: 4,5s. 3.16: 0,02rad/s
2
. 3.17: 140cm/s; 20cm/s.
3.18: a)
R2
|vv|
;
2
vv
v

2121
G

=
+
=
; b)
R2
vv
;
2
|vv|
v
2121
G
+
=

=
.
3.19: 4,4m; 2270 vũng; 76 vũng/phỳt. 3.20: 10Nm; 17,3Nm; 20Nm; 0Nm; 2Nm;
1,3Nm; kim ng h. 3.22: 4,6Nm. 3.23:
)RR(m
2
1
2
2
2
1
+

. 3.24:
2
mR
10
3
;
33
55
rR
rR
m
10
3


. 3.25:
2
mR
4
1
;
2
mR
2
3
. 3.26:
2
mR
2
1

. 3.27: a)
)rR(m
4
1
22
+
;
2
mR
16
5
; b)
22
22
22
rR
dmr
)rR(m
2
1

+
;
2
mR
24
13
. 3.28:
33
55

rR
rR
m
5
2


.
3.29:
2
ma
3
1
;
)ba(m
12
1
22
+
. 3.30:
2
m
3
1

. 3.31: a) 2m(a
2
+ b
2
); b) 2mb

2
; c) 2ma
2
.
3.32: a) 2ma
2
; b) ma
2
; c) 2ma
2
; d) 4ma
2
.
3.33:
R
r
cos;
R/Im
)cos(cosF
a
0
2
0
G
=
+

=
; <
0

: sang phi; >
0
: sang trỏi;
=
0
: quay ti ch. 3.34:
;
mm2
m2
ga
o
+
=

o
o
mm2
gmm
T
+
=
;
o
oo
o
o
m3m2
gm)mm(
T;
m3m2

)mm(2
ga
+
+
=
+
+
=
.
ẹAP SO CAC BAỉI TAP
346

3.35:
o21
21
m
2
1
mm
mm
ga
++

=
;
o21
21
m
2
1

mm
)cos(sinmm
ga
++
à+
=
. 3.36:
m3
F2
a =
.
3.37:
3
0
tb

=
. 3.38: 0,05Nm; 0,1Nm; 3.39: 34,6rad/s; 3.40:
t2
mR
0
2


Chng 4:
4.1: 10(kJ) 4.2: 0(J). 4.3: 17J. 4.4: 6J. 4.5: 25J 4.6: 16,7kW. 4.7: 36MW.
4.8:7200N. 4.9: 30km/h. 4.10: a) 2W; b)
2
kgmv
P

2
0
max
=
. 4.11: 396Nm.
4.12: 19,8kJ; 1320W. 4.13: 200W; 400W. 4.14: 500J; 250W. 4.15: 2kJ; 212kJ.
4.16: bỏnh . 17: 10kJ. 4.18: Nng lng tng tỏc. 4.19:
b
a2
r <
: y;
b
a2
r >
:
hỳt;
2
2
max
a27
b
F =
4.20: a) Khụng; b) Cỏc elớp; c) khụng, cỏc elớpxụit . 4.21: a) khụng
; b) cú. 4.22:
k4
mg3
;
k2
gmg3

;
k2
mg
. 4.23: r > r
C
: hỳt; r < r
C
: y. 4.24: H/2; H.
4.25:
3
2
;g3


. 4.26: 2,5; 2; 1;
)Rh(g
7
10

;
)Rh(g
3
4

;
)Rh(g
; qu
cu khi tr cỏi vũng. 4.27:
R
g

. 4.28: 15,5m/s. 4.29: 20%. 4.30: 6,25kW.
4.31:
2
m
kx
2
1
;
)xx(
m
k
22
m

. 4.32: 3kg. 4.33:
g2.)mM(
vm
2
22
+
. 4.34: .
4.35: 9kg; 1/9kg. 4.37:

+= j4i3v
H
h
k =
;
t
)gh2gH2(m

F

+
=

Chng 5:
5.1:
2,6.10
8
m/s.
5.2:
3,2.
5.3:

m = 8,6.10
-27
kg. 5.4: 8,19.10
-14
J. 5.5:
2,985m/s. 5.6: x = 137,7 km; t = - 374,7 às. 5.7: t
1
= 0; t
2
= - 2,5 às.
5.8
: a)
V =
rb
rb
tt

xx


= - 1,44.10
8
m/s
; b)
t
b
- t
r

=
4,39.10
-6
s = 4,39 às; c)
4,39às.
5.9:
u =

0,806 c.
5.10:
u = 0,946 c.
Chng 6:
6.3:

2
B
2
A

BA
SS
hg2
.S.SL


=
. 6.4:
gh2v =
. 6.5: 5m. 6.6: a) 20cm
3
; 10g; b) ni
lờn, chỡm xung; c) 666 kg/m
3
; d) k 1/3. 6.7: a) 600 lớt; b) lõu hn, vỡ vn tc chy
347
Giaựo Trỡnh Vaọt Lớ ẹaùi Cửụn
g
Taọp 1: Cụ Nhieọt ẹieọn

gim dn. 6.9: 5m; khụng. 6.10: 500N. 6.11:
2
2
2
2
1
2
1
t.
S

S
g
2
1
t.gH2
S
S
Hh +=
;
g
H
)12(
S
S
t
1
2
1
=
;
g
H2
S
S
t
1
2
2
=
. 6.12:

g'.
1
S
S
v
2
1
PP
h
2
B
2
A
2
AAo







+

.
6.13: c) H/2. 6.14: 700J. 6.15: a) 61,5%; b)
)(
)D(
V
211

12


=

Chng 7:
7.1: 29,5 lớt; 8,9 at. 7.2: 7,5 kg. 7.3: a)
1
2o
o1
2
V
pp
pp
V


=
; b)
21
2211
o
VV
VpVp
p
+
+
=
.
7.4: a)

a3
p
R3
p2
T
oo
max
=
; b)
aR.e
p
T
o
max
=
. 7.5:
omin
aTR2p =
. 7.6: 2.10
18
phõn
t/cm
3
. 7.7: 5,74 atm; an ton. 7.8: 1,83g/lớt.
Chng 8:
8.1: sinh cụng A =1000J; nhn nhit Q = 2500J. 8.2: sinh cụng A = 1184J; nhn
nhit Q = 1184J. 8.3: 30,8%. 8.4: 2324J. 8.5: 1454W. 8.6: 72J. 8.7: 150J; 90J. 8.8:
2,7kg; 25%. 8.9: 6,21.10
21
J.

Chng 9:
9.1: b) F
d
= 2,3.10
39
F
hd
. 9.2 = 4.10
16
rad/s; v = 2,2.10
6
m/s. 9.3: thiu 1,25.10
13

electron. 9.4:
1
21
2
21
2
F
qq4
)qq(
F
+
=
. 9.5:
7
mgtg
q sin 1,1.10 C

k


= =
.
9.6: a) 1,35.10
5
V/m; b) 3,1.10
4
V/m; c) 1,92.10
4
V/m; d) 1,5.10
4
V/m; e) AN = 20cm,
BN = 40cm. 9.7:




=




d
'rr
)'rr)('r(
4
1
)r(E

)(
3
o

,




=




d
'rr
)'r(
4
1
)r(V
)(
o


9.8: a) E
x
= -2ax; E
y
= -2ay; E
z

= -2bz; b) nhng elipsoid trũn xoay. 9.9:
r
r
.
2
E
o
o




=
;
V =
0
0
rC
2

+

. 9.10:
22
o
hah2
a
E
+

=
;
22
aah
V2kln
h

++
=



.
9.11: a)E
A
> E
B
; V
A
> V
B
; b) E
A
> E
B
; V
A
< V
B
; E

A
= E
B
= E
C
; V
A
= V
C
> V
B
.
9.12 : 45
0
. 9.13 : a)A
BC
= A
AD
= 0; b) A
AC
= A
DC
; c) khụng thay i.
9.14: E
A
= E
B
; V
A
= V

B
; A
AB
= 0. 9.15 :
2k sin
E
R

=
; V = 2k.