đáp số bài tập vật lý đại cương 1

343 Giaựo Trỡnh Vaọt Lớ ẹaùi Cửụng 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 Cửụng 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
r
R
ar
OG

=
;
6
R
OG =

.
3.11:
33
3
r
R
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
r
R
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
r
R
dmr
)rR(m
2
1

+ ;
2
mR
24
13
. 3.28:
33
55
r
R
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:
t
2
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 Cửụng 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)
a
R
.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.
ẹAP SO CAC BAỉI TAP 348
9.16 : a)
11
E2k||
x2ax

=+



;
2a x
V2k||ln
x


=



b)

22
4ka | |
E
ah

=
+
; V = 0
Chng 10 :
10.2 : a) 8,85pF; b)
a)ad(
S
C
o
+

=
; c)
a
d
S
C
o


=
. 10.3 : a) Q = Q
o
= C
o

U
o
;
C =
o
C
2
1+
; U =
o
U
1
2
+

; b) E =
d)1(
U2
o
+
; c) Q
chỡm
=
o
Q
1
+


;

d)
0
C)1(2
Q)1(
W
o
2
o
<
+

= . 10.4: a) C = 8àF; Q
1
= Q
2
= Q
3
= 44àC; Q
4
= 132àC; b) 8
cỏch. 10.5: - 19,2àJ. 10.6: a) Q
1
= 48àC, U
1
= 12V; Q
2
= 72àC, U
2
= 12V b) Q
1

=
16àC, Q
2
= 24àC; U
1
= U
2
= 4V. 10.7: C
2
= 5àF.
10.8: a) K m:
43
43
21
21
CC
CC
CC
CC
C
+
+
+
=
, Q
1
= Q
2
=
U

CC
CC
21
21
+
, Q
3
= Q
4
=
U
CC
CC
43
43
+
; b) K úng:
4321
4231
CCCC
)CC)(CC(
C
+++
+
+
=
,
4321
421
1

CCCC
U)CC(C
Q
+++
+
=
,
4321
312
2
CCCC
U)CC(C
Q
+++
+
=
,
4321
423
3
CCCC
U)CC(C
Q
+++
+
=
,
4321
314
4

CCCC
U)CC(C
Q
+++
+
=
;
e
U
.
CCCC
CCCC
n
4321
3241
e
+++

=
;
4
2
3
1
e
C
C
C
C
0n ==

.
10.9:
o
o
U
C
C
U =
= 8000V. 10.10: U
BA
= 2V. 10.11: Q = 1,59àC; Q = 10,6àC.
10.12:
U2
mgd
q =
. 10.13: U = 20V. 10.14:
cm1,2)2s(
U4
Us
x
o
=+=
.
10.15:
2
2
o
dU2
U

.
Chng 12 :
12.1 : a)
)ba2ba(S
ba)ba(
R
22
22
+++
++
=
;
b)
S
a
.
)ba2ba)(ba(
)baba(bba)ba(
R
22
2222

++++
++++++
=
;
349 Giaựo Trỡnh Vaọt Lớ ẹaùi Cửụng Taọp 1: Cụ Nhieọt ẹieọn
c)
S
.

ba2ba(
ba)ba(ab2
R
22
22

+++
+++
=
.
12.2 : I = 3A, U
AB
= 1,5V; a) K m: Q
1
= Q
2
= 0,3àC, U
1
= 1V, U
2
= 0,5V; b) K úng:
U
1
= 0,9V, Q
1
= 0,27àC, U
2
= 0,6V, Q
2
= 0,36àC.

12.3: I
1
= 1,5A, I
2
= 2,5A, I
3
= 4A; U
1
= 1,1V, U
2
= 1V, U
3
= 1,2V.
12.6: s a: R = 15; s b: R = 5. 12.7: K m: U = 2V, lch sang phi; K
úmg: U = 1,86V, lch sang phi. 12.8: a) 6 búng; b) 23A. 12.9: a)
781
A; A; A
999
;
b)
12 21
12
Er Er
E1,7
rr
+
==
+
5V
v

12
12
rr
r0,25
rr
=
=
+
; c)
21 12
12
Er Er
R1
2(E E )
,75
+
=
=

;
d)
2
12
Er
R1,
EE
==

5
; e)

1
1
1
E
I4
r
==A
,
2
2
2
E
I3A
r
==

12.10: a) I
1
= 1,2A (ngun thu), I
2
= 0,4A (ngun phỏt), I
3
= 0,8A (ngun phỏt); b) U
1

= 4,8V, U
2
= 1,2V, U
3
= 5,6V; c) Cụng sut tiờu th ca ngun 1: P

1
= 13,44W, hiu
sut np in: H
1
= 89,3%; P
2
= 8W, H
2
= 96%; P
3
= 24W, H
3
= 92%; d) oo cc
ngun E
3
thỡ c 3 ngun u phỏt: I
1
= 0,8A, I
2
= 2A, I
3
= 2,8A; U
1
= 3,2V, U
2
= 6V,
U
3
= 19,6V; P
1

= 8W, P
2
= 40W, P
3
= 84W; H
1
= 92%, H
2
= 80%, H
3
= 72%.
12.11: a) U = 22V; b) U = 12,2V; c) U = 9,6V, U = 2,44V; d) 92mA, 18mA.
12.12 : I
1
= 3,01A; I
2
= 2,78A; I
3
= 1,93A; I
4
= 1,08A; I
5
= 0,23A; I
6
=0,85A.
12.13: Q
1
= 2,5àC; Q
2
= 2,25àC; Q

3
= 0,25àC. 6.14: U = 50,8V; I tng, U gim.
12.15: a) A = Q = 60J; b) A = 60J, Q = 21J. 12.16: 2kW. 12.17: a) 6 dóy //, mi dóy
10 ngun; P
max
= 65,25W; b) cú 6 cỏch mc: 3, 4, 5, 6, 10, 12 dóy //.
12.18: a) Cn ớt nht 6 ngun mc theo 2 cỏch sau: C1: mc ngun thnh 1 dóy 6
ngun ni tip v mc ốn thnh 2 dóy //, mi dóy 4 ốn; C2: mc ngun thnh 2 dóy
//, mi dóy 3 ngun v mc ốn thnh 4 dóy //, mi dóy 2 ốn; b) 20 ốn, mc theo 2
cỏch: C1: mc ngun thnh 1 dóy 15 ngun ni tip v mc ốn thnh 2 dóy, mi dóy
10 ốn; hoc mc ngun thnh 5 dóy, mi dóy 3 ngun v mc ốn thnh 10 dóy, mi
dóy 2 ốn. 12.19: a) 4; b) 2,4; 50%; 5,6, 64,3%; c) 1,2A. 12.20:
4 cỏch; 8 cỏch.
12.21: Loi 3: 5, 10, 15 cỏi v tng ng loi 5: 8, 5, 2 cỏi. 12.22: loi (5, 3,
1/3) cú (4, 18, 78) hoc (8, 11, 81) hoc (12, 4, 84) cỏi. 12.23: 5 cỏi; 6 cỏi.
Chng 13:
13.1: a) B = 0; b) B = 5,7.10
5
T. 13.2: M thuc on I
1
I
2
, cỏch I
2
l d/3; M nm ngoi
on I
1
I
2
cỏch I

1
v I
2
ln lt l 2d v d. 13.3: H = 31,8A/m. 13.4: a) B
O1
= B
O2
=
2,1.10
- 5
T; B
M
= 1,4.10
5
T ; b) B
O1
= B
O2
= 1,7.10
5
T; B
M
= 0. 13.5: B = 6,8.10
5
T.
13.6: a)h = 0; b) H = 79,6A/m. 13.8: F = 2,45N. 13.9: F = 0,8N. 13.10: a) theo chiu
KH; b)

à
=

2
2lnaI
oo
m

; c) Khung dõy b kộo cng v tin v gn I
o
bi lc kộo

à
=
4
II
F
oo
. 13.11: v = 36,3.10
6
m/s; W

= 6,2.10
6
J; T = 5.10
9
s; L = 9,9.10
6
kgm
2
/s.
13.12: v
o

= 7,6.10
6
m/s. 13.13: b) v = 2.10
6
m/s theo phng vuụng gúc vi v ;

B

E
ẹAP SO CAC BAỉI TAP 350
c) r = 2,3 cm.
13.14: a) 25,12.10
5
Wb; b) 5,02.10
4
J. 7.15: b) v = 0,67mm/s; n
o
= 2,8.10
23
ht/cm
3
.
Chng 14:
14.1: a) U = 0,5V; b) U = 0,25V. 14.2: a) E
o
= 1,23V; b)

= BScost.
14.3: U = 0,25V; u cỏnh trỏi cú in th cao. 14.4: a) 10
7

W; b) 0,04àC.
14.5: I
max
= 1,6A. 14.6: B = 0,3T.
14.7: E
c
= 0,3V; b) I = 10A; c) F = 3N; d) P
c
= 3W; e) P

= 2W; f) P
n
= 5W.
14.8: cd qua hai thanh kim loi:










++

=
2
t
t2r4

BD
I
22
; cng dũng in qua
hai on vũng dõy:


=
2
t
II
1
;




=
2
t2
II
2
.