ĐỀ CƯƠNG BÀI GIẢNG VẬT LÝ ĐẠI CƯƠNG A1 (TÀI LIỆU DÙNG CHO SINH VIÊN ĐHSP TIN HỌC )

1

TRƯỜNG ĐẠI HỌC HÙNG VƯƠNG

VẬT LÝ ĐẠI CƯƠNG A1

MỤC LỤC
2


CHƯƠNG 1
Động học chất điểm
 !"#$%&'(!") !*+,  /&012'-3") !
*) Môc tiªu:
)4 5'67899:9;&: 3 <=>,6?9@73A9B+033&79&'(536C3A/&<D'(9& !'/>-39/A E
9@13A9&'(536C3A&F3A>,9&'(536C3A913A4
$4 5'67899:9;&: 3 <=.&7B3A@G3&9&'(536C3A/.&7B3A@G3&D'H6I19JE9&K6 5=4
L4 &M3+ <67899:9NI3A9&'(536C3A>,>-3NO3A67899:99P3A&Q99&1R3ANI3A
9&'(536C3A4
1.1. Sự chuyển động của vật. Hệ qui chiếu. Vận tốc - gia tốc
)4)4)4&'(536C3A>,&<D'(9& !'
&'(536C3A9JE=C>-2,ST9&'(53NU >V@W9JE>-6X6 >Y 9:9>-;&:9@13A
;&P3AA E3>,&U A E34AZ==C&<@O9[E6C>Y A9[E6C>,=C6Z3A&Z
>Y A9&U A E3
)4)4$4&K6 5=>,&<9&K6 5=
 &K6 5=2,=C>-9X;W9&&7Y93&\;&P3A6:3A;5S1>Y 3&]3A;&103A9:9&/3&]3A
;W9&&7Y9=,E6E3A;&01S:4
)4)4L4&7B3A@G3&9&'(536C3A9JE9&K6 5="
^& 9&K6 5=_9&'(536C3A/9:9[E6C9JE3X2,9:9&,=9JE&U A E3"
 *  *          = = =
  )`)

E("
   =
r r
)`$
[ 2, !"#9JE9&K6 5=_4
)4)4a4b'H6I1
$%"&'9JE9&K6 5=9&'(536C3A2,67U3AI1+c  &8.
K909:9>V@W9JE3X@13A;&P3AA E34
)4)4d41,3&6C913A
 0& !9&K6 5=_9&'(536C3A@e39'3Af_;W& <'2,"
¼
() *=
/A[ 2,'+"#',-)^& _9&'(536C3AS2,&,=
9JE&U A E3"SgS  )`L
)4)4h4-39
./01-:-39@'3A+G3&9JE9&K6 5=@13A;&103A&U A E3∆2,"

2
*


∆
=
∆
uur
r
)`a
?9@73A9&16C3&E3&`9&-=@'3A+G3&9JE9&'(536C3A
9&K6 5=@e3
¼

i))
456?9@73A9&16C3&E3&9&-=I R3A&U
6 5=/Ejk∆>P9l3A3&\"
 3
* 4*
 56
 4
∆ →
∆
= =
∆
uur uur
r
)`d
,78A[ m2,99JE9&K6 5=I &U 6 5=4:3;<"!6
!"#'=4 ,-1"&'>3;<"!6!"#'= ?5&
@0",-A"0"#-6,-!"#&B8"!6
3
.C n9B>-39I =C>V@W_2,=C>n9B
v
9X.&7B3A3o=@e3 !.
'(!3>Y D'H6I1I _/9X9& p'&n19& p'9&'(536C3A>,9XA :@V+o3A@V'(<6 "
dt
ds
v =
)`h
.D'E-"#/FA E&K(
dsdr ≈
/3e3)`h9X&5> !"
dt

dr
v =
-("
222
2
z
2
y
2
x
dt
dz
dt
dy
dt
dx
vvvv






+







+






=++=
)`q
)4)4q4 E9
G/01-+2!7,-- C+ !3& e3@'3A+G3&9JE>n9B>-39
@13A=C6B3>V&U A E3&n16V3&3A&rEA[ 2,-29JE9&'(536C3A@13A
;&103A&U A E3∆>,6789;W& <'"
i
2
  
-
 
− ∆
= =
∆ ∆
ur r uur
uur
)`s
-78A[ m2,-99JE9&K6 5=I &U 6 5=/>,6789;W
& <'2,"
t
v
lima
0t

∆
∆
=
→∆

4
4
=
uur
4
C2Y3A E9"
2
2
2
2
2
2
2
2
2
2
z
2
y
2
x
dt
zd
dt
yd

dt
xd
aaaa






+






+






=++=
)`t
GH-+-A
-H-

4
-

4
=
uur
ur
)`)#
-IJ KL,-1"&'&)J=5+
=!"#MN+= ?5&MO6J"#5L2P"&'+6"#5L
'8-
2H-A
$


-
Q
=
)`))
 E9.&:.'(!36?9@73A9&1ST&E(6u .&7B3A9JE>n9B>-394
 -(/A E9"
3
EEE +=
)`)L4/#5L
$
$
$
$
3
$

v
>

N
N>
EEE






+






=+=
)`)$
)4)4s4-39>,A E9@13A9&'(536C3A@w3
RJ
-39AX9@'3A+G3&@13A;&103A&U A E3∆"

+
∆
θ∆
=ω
4 )`)L
-39AX99JE9&K6 5=I &U 6 5="
N
N

θ
=ω
/6B3>VvEN E3xS@ENxS )`)a
 >Y 9&'(536C3A@w36p'
ω
g913S/9&';G"
ω
π
=
$

 )`)d
4
D-J
y3S2,S9&';G@13A=C6B3>V&U A E3"

@ 
ω
ν
π
= =
)`)h
n9B>-39AX9
ω
A[ 2,>n9B>-39AX9/3o=@e3@O99JE>w3A@w3D'H6I1/
&'-39& p'6 >Y 9& p'D'E(9JE9&'(536C3A>,9XA :@V+o3A
ω
4
O e3&<A ]E
ω

>,>n9B>-39N, 
→
v
9JE9&'(536C3A"
ω=>
vΛ
 )`)q
O$4 e3&<A ]EE
3
>,
ω
"
$


-
Q
=

gv4
ω
$
)`)s
RH-J  E9AX9@'3A+G3&@13A;&103A&U A E3∆"

+
∆
ω∆
=β
 )`)t

 E9AX99JE9&K6 5=c&U 6 5="


#
∆
ω∆
=β
→∆
lim
g
$
$
4 4
4 4
ω θ
=
@ENxS
$
)`$#
&-3jk"!'βg913S/E9X9&'(536C3A
@w3&E(6u E9&Q3A= 3&67899:9&<&Q9"
ω
 g β  z 
ω
#
* θ g 

$
)
#

$
ω+β
* 
βθ=ω−ω
$
$
#
$
4
-J"o=@e3@O99JED'H6I1
@w3/9l3A9& p'>Y 
ω
;& β{#>,3A7892I ;& β|
#/9XA :@V+o3Aβ4&7>-(E9X&5> !&<&Q9>n9B3&7SE'"
dt
d
ω
=β

)`$)
O e3&<A ]E>n9BA E9AX9>,>n9BA E9 !.'(!3"
 

4 Q 4
- Q Q
4 4
ω ω
β
= = =
)`$$

E&K(@o3A@13A=[ @7U3A&8.+E>n9B
t
a
/
β
>,
R
&n1&QT6XI1&,3&=C
E=N <3&'-3/3e3E9X&5;!2'-3"
vE

∧β=
  )`$L
1.2. Một vài dạng chuyển động đơn giản
&'(536C3A&F3A+ !36u 6p'>,NE16C3A6 p'&wE&F3AST 8EU"E9
1.3. Bài toán động học
&T93A& <=9&Q3A\@o3A@13A=C.&I=> ;&P3A2Y32m=/=[ 9&K6 5=6p'@B >Y
9l3A=CA E9A&n1.&7B3A&F3A6Q3A&7Y3Aj'3AN7Y >,A :@V;&P3A6u 4
^&01S:9&'(536C3A9JE=C9&K6 5=j'K.&:R=C6 5=@e3=?6K>Y >n9B
>-39+E36y'2}9g#&8.>Y =?.&F3A3o=3AE3A=CAX9α+, 1:3+m3.&:1/2
.&7B3A@G3&9&'(536C3A/.&7B3A@G3&D'H6I1/y=jE>,y=9E1
*) Tài liệu học tập chương 1
)47B3A'(e3G3&)ttt/5V"& / )/&,~'K+03 :1NO9/,C 4
$47B3A'(e3G3&$##)/W+5X"& ; )/&,~'K+03 :1NO9/,C 4
*) Câu hỏi ôn tập và bài tập chương 1
5
Câu 1. &7B3A@G3&9&'(536C3A>,D'H 6I19&'(536C3A2,AG•T;&:93&E'A ]E9&}3A•
e'9:9&G=.&7B3A@G3&D€(6I14
Câu 2. &M3+ <>-39@'3A+G3&>,>-39Q9&U •e'%3A&rE>-2%9JE9&}3A4
Câu 3. V3&3A&rE>,3e'%3A&rE>-2%9JEA E9•I SE1.&0 67E&e=;&: 3 <=A E9

 !.'(!3>,A E9.&:.'(!3•
Câu 4. R6V3&3A&rEA E9&•(S'(@E9:9NI3A9&'(536C3A9X&59X4
Câu
5. G= 9:9 + 5' &Q9 >-3 9 AX9/ A E 9 AX9 @13A 9&'(53 6C3A @w3/
.&7B3A@G3&
9&'(536C3A@13A9&'(536C3A@w36p'>,@w3+ !36u 6p'4
Câu 6. &'(536C3A&F3A&E(6u 6p'2,AG•&M3+ <9:9@7U3A&8."Eg#/E{#/E|#4
Bài 1.1. _C9& !9PP9&'(536C3A@e3=C67U3A@w3+:3;W3&d#=4b'•3A67U3A6 6789
@e3D'H6I19X9P3A&Q9"g`#/d
$
z)#z)#=4G=>-39/A E9 !.'(!3/A E9.&:.
'(!3>,A E91,3.&y39JEPP2}9gdS4B3>V9JED'•3A67U3AS2,=k=4
Bài 1.2. _C>-67893k=2e3R=?6K&n1.&7B3A&F3A6Q3A>Y >-39+E36y'
>
#
g$#=xS4\D'ESQ99039JE;&P3A;&W/2K(A E9@[3A@7U3AAg)#=xS
$
4
E4W3&6C9E19T96I 9JE>-6X>,&U A E3656 2e367896C9E16X4
+4R6C9E19T96I >-@B Y =?6K&!+E12M'•W3&>-399JE>-;& >-9&I=6K4
Bài 1.3._C>P2‚3A6E3AD'E(>Y >-39L##>w3Ax.&}&G+V&•=2I 4E'=C.&}>-39
9JE>P2‚3A9w32,)s#>w3Ax.&}4
E4W3&A E9A99JE>P2‚3A2}9+V&•=4
+4W3&S>w3A>P2‚3AD'E(6789@13A=C.&}+V&•=6X4
Bài 1.4._CPP9&I(@e367U3A&F3ARf6!3>Y >-39>
)
ga#^=x&/@Z D'E(2I f>Y
>-39>
$
gL#^=x&4W3&>-39@'3A+G3&9JEPP@e3D'•3A67U3A;&Q&Z 6X4

Bài 1.5.@13A3A'(e3ƒ(N@1/E9X&591 n2n9@139&'(536C3A@w36p'j'3AD'E3&&I
3&M3  >Y  +:3  ;W3&  D'r  6I1  2,  v  g  #/d4)#
`s
9=  >,  >-3  9  9JE  n2n9@13  @e3  D'r  6I1  2,
>g$/$4)#s9=xS4G="
E4-39AX99JEn2n9@13@13A9&'(536C3Aj'3AD'E3&&I3&M3/
+4&U A E33XD'E(6789=C>w3AD'E3&&I3&M3/
94 E9.&:.'(!39JEn2n9@13@13A9&'(536C3Aj'3AD'E3&&I3&M34
6

CHƯƠNG 2
Động lực học hệ chất điểm
 !"#L%&'(!"$ !*+,  /&012'-3") !
*) Môc tiªu:
)4 5'>,>-3NO3A67899:96V3&2'-n„13///9:96V3&2%>p6C3A2783A>,6V3&2'-
+011,36C3A2783A/>-3NO3A678965A 0 9:9+,  4
$4 5'67893A'(e32%7B3A6 E2 2k1/>-3NO3A67892T9D':3W3&@13A&<D' 9& !'9XA E
965A 0 &W9&9:9& <3783A&T9!>,A 0 9:9+,  4
L4 5'>,>-3NO3A9:96V3&2W>p6C3A2783A/=P=n36C3A2783A/6C3A3‚3A>,9B3‚3A65
A 0 9:9+,  4
2.1 Các định luật Newton (Newton)
$4)4)4V3&2'-n„13&Q3&K
Y6#<"!6Z5;&P3A9&V'=C:96C3A3,1R+e33A1, "-"7
F;J*[\"7F;"-!"#!"#,-J5+]"=
W3&9&K+011,3@I3A&: 9&'(536C3AA[ 2,AX;>G>-(6V3&2'-n„139w3
A[ 2,"05AX
$4)4$4V3&2'-n„13&Q&E 
 E99&'(536C3A9JE9&K6 5=…2<>Y u3A&8.2T9:9NO3A
F
>,…2<3A&V9&>Y

;& 2783A9JE9&K6 5=K(/@13A&<"
m
F
a =
$`)
$4)4L4&7B3A@G3&9B+039JE9B&[99&K6 5="
&7B3A@G3&n„13"
Fam =
2,.&7B3A@G3&9B+039JE9B&[99&K6 5=4&7B3A
@G3&  3,(  &M'  X=  90  &E  6V3&  2'-  n„13    >,  4  Y  6V3&  2'-  n„13  "
913S>#E#† =→=→=
*6V3&2'-n„13"
#
=
†
E#† ≠=→≠
4
$4)4a4<D'(9& !'D':3W3&
&T93A& <=9&Q3A\@o3A.&7B3A@G3&$`)9&…3A& <=6}3A6 >Y 3&]3A&<D'(
9& !'6?9+ <A[ 2,AX4,&<D'(9& !'@13A6X9:96V3&2'-n„13
67893A& <=6}3A4@13A&T9!/;& ;&P3A9y36C9&W3&j:99E1/&G3A7U E9X&591 &<D'(
9& !'6Q3A(e3&1?99&'(536C3A&F3A6p'6 >Y @: 6K2,&<D'(9& !'D':3W3&4
$4)4d4V3&2'-n„13&Q+E
Y<"!6(A4\5F<"!6W6#5U
F
<"!6W^A4\5F
<"!6(6#5U
'F
"-5U
F

>,
'F
_&"_8K ; ?=+K
 8"#
O@`A#5U,-6#<"!6Z5SaE5+MX92PMZ
2.2 Nguyên lí Galilê
$4$4)4^&P3AA E3>,&U A E3&n19B&[99u6 534
 <j(‡6Q3A(e3>,&<ˆjˆ(ˆ‡ˆ9&'(536C3A6p'
N[9&n1jS1>Y &<*
Y =‰ &<[E6CEAm3>,1=C6Z3A&Z659&…&U
A E34E&•(jk=C6 5=_+K;Š"I =C2}99&…+c 6Z3A
7
&Z9JE&</_9X[E6C@13A&</2,j/(/‡*@13A&<ˆ2,ˆ/jˆ/(ˆ/‡ˆ4&n19:9D'E36 5=
9JEn„13"
E &U A E39XW3&'(<6 ;&P3A.&O&'C9&<D'(9& !'"gˆ/
+V@W9JE_@13A;&P3AA E32,7B3A6 4
9^&103A9:9&A ]E&E 6 5=+K;G@13A;&P3AA E32,'(<6 4
$4$4$4T9D':3W3&
T9
†
D
g`=
-
r
A[ 2,5UAXT9D':3W3&2,=C2T9019&…D'E3S:6789@13A
&<D'(9& !';&P3AD':3W3&4T9D':3W3&2'P32'P3K >, ?=L-
!"#,-MZAX
2.3. Các định lí về định lượng, mômen động lượng, động năng và cơ năng
$4L4)4:96V3&2W>p6C3A2783A
R6V3&2'-n„13/S'(@E"

4
6
4
=
r
4S 6 9 4S Y 9
b
4 4
= =
r ur
ur
$`$
n9B
>=^ =
A[ 2,"#5 ?9JE9&K6 5=4
/05X/&'+6"#5 ?,-6#<"!6"L8-JA02P5US'c
`?A5U9A4\5F<"!6"J
R$`$S'(@E"
∫
=−=∆
$
)


)$
N†^^^ .
   $`L
[ 2,5 ?9JE
F
@13A;&103A&U A E3R

)
6!3
$
4
/05X"/#2F"#5 ?,-6#<"!6'6#M'O8-JA0
2P5 ?,-5US-`?5U9A4\5F<"!6'M'O8-"J
@13A@7U3A&8.
†
;&P3A6u &n1&U A E3E9X"
†

^
=
∆
∆
  $`a
-("/#2F"#5 ?,-<"!6'"08-JA02P5U
A4\5F<"!6"J
^& @E;&\ .&I=> 9JE9B&[9n„139:99P3A&Q9@e3>‹36}3A4G>-(E9X&53X
@o3A">p=C=?3,16X9:96V3&2W>p6C3A2783Au3AD':&B36V3&2'-n„134
$4L4$4Œ3A&rE9JE6C3A2783A>,j'3A2783A
d1-,-"#5 ?_Q96C@'(p39&'(536C3AR=C>-3,(SE3A>-;&:9.&O
&'C9>,190&E W3&9&K9JE>-&Q3&K2,>-39>,;& 2783A4X 9:9&;&:9/>-39
;&P3A6?9@73A&1,31,39&19&'(536C3A>p=?6C3A2T9&[94&W3&6C3A2783A/6I 2783A
;!&8.90;& 2783A>,>-39/=Y "c 'MON!"#=6c"#5U
E
d1-,-5 ?e5 ?,-6#5U'M'O8-
∆
"c 
'A4\,-5U'M'O8-"J4&WNOj:9&SP37Y9/E(E=\ +c &E (!'

2,;& 2783A37Y9>,&U A E3j:9&SP4
$4L4L4V3&2W>p=P=n36C3A2783A
~k=C9&K6 5=_9&'(536C3A@e3D'H6I1N7Y :9NO3A9JE=C2T9 
F
4R
.&7B3A@G3&$`$/+ !36u /E&'6789"
†@^@
N
N
∧=∧ )(
 $`d
8
Y "
 @ ^4= ∧
ur r uur
,6Z6"#5 ?9JE9&K6 5=6 >Y 6 5=4w3W9&
&]'&7Y3A
†@ ∧
2,=P=n39JE2T9
†
6 >Y g
)(/ †1m
&E(;W& <'2,
)
uur
&7B3A@G3&$`d9X&5> !"
4f
)
4
=

uur
uur
 $`h
V3&2W>p=P=n36C3A2783A/&'+6'8-,-6Z6"#5 ?"Lg
,-6#<"!6!"#2P`6Z6"Lg,-A5UA4\5F<"!6
O@13A@7U3A&8.9&K6 5=9&'(536C3A2'P32'P39&V':9NO3A9JE=C2T9
j'(e3M=.&7B3A9JE2T9:9NO3A 
†
 2'P32'P36 D'E96V3&&G 
)
uur
 2'P32'P3+o3A
;&P3A/N16X
=⇒= #
N
N
&o3AS4 $`q
&7B3A@G3&$`q2,3C N'3A9JE6V3&2'-+011,3=1=n36C3A2783A4
G
L
2'P32'P3>'P3AAX9>Y =?.&F3AI1+c >,>n9B
Y
ur
4X 9:9&;&:9=?.&F3A
3,(2,=C=?.&F3A96V3&/3e3<"!65Z5Z!"#'6#6c]"0
$4L4a4C3A3‚3A9JE9&K6 5=
_C9&K6 5=/6E3A9X>-39
)
>
>,9&V':9NO3A9JE2T9

†
+K;G9&1Y ;& 3XY >V
@W$>Y >-39
$
>
4R6V3&2'-n„13+ !36u E6789"
$
=>
$
=>
$
=>
NSN†
$
)
$
$
$
)
>
>
$
$
)
−=







=
∫ ∫
.
 $`s
783A
$
=>
$
"2,6C3A3‚3A9JE9&K6 5=/2,=CS619JE9&'(536C3A/3X6?9@73A
9&1NT@]3‚3A2783A9JE=C>-6E3A9&'(536C3A4-(/6V3&2W+ !3& e36C3A3‚3A" /#
2F"#N,-<"!6F6#h" 8"2PZ,-5UA4\5F
<"!6Fh" 8""J
$4L4d4B3‚3A
DiIN,-<"!6
&}3AE+ !@o3A6C+ !3& e36C3A3‚3A9JE3X+o3A9P3A9JE2T9:9NO3A4P3A3,(
+E1AZ=9P3Af

9JE9:92T9&!>,9P3Af
;
9JE9:92T9;&:9;&P3A.&0 2T9&!4
E> !6789"f

zf
;
g•
6$
Ž•
6)
/=?;&:99P3A9JE9:92T9&!+o3A6CA 0=&!3‚3A/

3e3"`f

g•
$
Ž•
)
4'(@E"f
;
g•
6$
z•
$
`•
6)
z•
)
g•
$
Ž•
)
4
@13A6X•
)
/•
$
u3A9JE6C3A3‚3A>,&!3‚3AcR3A>V@W)>,$6789A[ 2,9B3‚3A
9JE>-c>V@W)>,$4&7>-(/"#2FN,-<"!62PZ,-A5U
MAMZO5+5UA4\5FJ4!'9&K6 5=9&…9&V':9NO3A9JE9:92T9&!&G
f
;

g#>,"•
)
g•
$
g•g913S4V3&2'-+011,39B3‚3A9JE9&K6 5="Y5UA4\5F
<"!6j5+5U;N,-<"!65+6#"&5 ?MZ"`
DiIN,-
~k=C&<AZ=39&K6 5=9X;& 2783A=
)
/=
$
/444>,9&…9&V':9NO3A9JE9:92T9&!4
R6V3&2'-n„13&Q&E />,6?g
∑
=
3
)
•
6
2,6C3A3‚3A>,g
∑
=
3
)
•

2,&!3‚3A9JE9B&<
E67896V3&2'-+011,39B3‚3A9JE9B&<4"Nzg#&E(zg•g913S $`t
9
!'3A1, 3&]3A2T9&!9B&<9w39&V':9NO3A9JE3&]3A2T9;&:9;&P3A.&0 2T9&!4

&GE@}@E6789: NzgNf
;
4•6M(Nf
;
2,9P3A9JE9:92T9;&:9;&P3A.&0 2T9&!:9
NO3A2e39B&<@13A;&103A&U A E3N/3e3"NzgN• $`)#
-("/#2FN,-'6#M'O8-2PZ,-5U
MAMZO5UA4\5F'M'O8-"J
*) Tài liệu học tập chương 2
)47B3A'(e3G3&)ttt/5V"& / )/&,~'K+03 :1NO9/,C 4
$47B3A'(e3G3&$##)/W+5X"& ; )/&,~'K+03 :1NO9/,C 4
*) Câu hỏi và bài tập chương 2
Câu)4&M3+ <ST;&:93&E'A ]E&E &<"•&<;&P3A9&V':9NO3A‘>,•&<9&V':9NO3A9JE
9:92T99M3+o3A3&E'‘4<3,1678991 2,9P2 4
Câu$4e'%3A&rE9JE2T9>,;& 2783A4&:+ 5'6V3&2'-n„13&Q&E 4@[3A2783A2,AG•
&M3+ <@[3A2783A>Y ;& 2783A4&:+ 5'6V3&2'-n„13&Q+E4e'%3A&rE9JE3X4
CâuL4&Q3A= 3&9:96V3&2%>p6C3A2783A>,j'3A2783A9JE2T94e'%3A&rE9JE9:96I
2783A3,(4
Câua4& !2 6V3&2'-+011,36C3A2783A4 0 &W9&& <3783AS}3AA -2l ;& +m34
Câud4e'6 p'; <39y3& !659&K6 5=9&'(536C3A913A4T92(M=2,AG•X3&]3A21I
2T9=ES:3,1/> !+ 5'&Q99JER3A21I 2T9=ES:4
Câuh4T9D':3W3&2,AG•e'>, >WNO>p2T93,(4&M3+ <2T9D':3W3&2(M=>,2T92(
M=4e'>WNO= 3&&[E>p@I3A&: ‚3A@[3A2783A/A 0=@[3A2783A>,;&P3A@[3A2783A4
Câuq4B&[99u6 53D'E33 <=3&7&!3,1>p;&P3AA E3/&U A E3•
Bài 2.1._C>-3?3A3&\@78;&P3A=ES:R6…3&f9X6C9E1&
)
j'3A9&M39JE=?
.&F3Af3A& e3A=CAX9’gad
#
S1>Y =?.&F3A3AE3A4CN, 9JE=?f2,S

)
g$/##=4
W3&>-39>
)
9JE>-3?3A;& 3XY 9&M39JE=?3A& e3Af4K(A E9@[3A@7U3A
Agt/s=xS
$
4E'6X/>-3?3A !.O9@78;&P3A=ES:>Y >-39>
)
R9&M32e3.&WE@e3
9JE=?.&F3A3A& e3A=CAX9“gL#
#
S1>Y =?.&F3A3AE3A4
W3&6C9E1&
$
Q3A>Y >V@W9E13&K9JE>-3?3A@e3=?3A& e3A41S:3&&
)
>Y &
$
4^!
D'0G=67899X.&O&'C9>,1’>,“;&P3A•
Bài 2.2._C,'6 <39&I(@e361I367U3A&F3A3AE3A>Y A E9;&P3A6u 2,#/$d=xS
$
4E'
a#S;5R2}9;&c &,3&/3A7U Em6C3A9B>,,'6 <39&I(9&-=Ny36p'Y ;& NR3A&F34
<S=ES:A ]E+:3&jn>,67U3A@E(2,#/#d4K(Agt/s#=xS
$
4•(j:96V3&"
E4-392Y33&K>,A E99&'(536C3A9&-=Ny36p'9JE,'6 <34
+4&U A E39&'(536C3A9JE,'6 <3>,61I367U3A,'6•6 67894

Bài 2.3._C+03A‰f67896?@e3=C=?.&F3A3A& e3A&8.>Y =?.&F3A3AE3A=CAX9’
gL#
#
4l3A=CS8 NM(=03&;&P3AN•3>mD'E@w3A@[9v/=C6y'NM(+'C9>,1+03f/6y'
NM(9w32I +'C9>,1+03A‰4^& 2783A9JE+03f2,=
)
g)/#;A>,9JE+032,=
$
g)/d;A4
<S=ES:9JE=?3A& e3A2,;g#/$#4\D'E;& 2783A9JE@w3A@[9>,=ES:9JE@O9D'E(4
K(Agt/s#=xS
$
4•(j:96V3&" E99JE9:9+03A‰f>,/>,T99‚3A9JES8 NM(
Bài 2.4._CS8 NM(>mD'E=C@w3A@[9r3&v)>,=C@w3A@[96C3Av$4_C6y'S8 NM(
+'C996V3&I 6 5=>,6y'; E@n1=CD'03?3A;& 2783A=
)
4_CD'03?3A;&
2783A=
$
6789@n1>,1@w3A@[96C3Av$4\D'E=ES:/;& 2783A9JE9:9@w3A@[9>,9JE
S8 NM(4K(A E9@[3A@7U3AAgt/s#=xS
$
4•(j:96V3&A E99JE>-=
$
>,2T99‚3A
9JES8 NM(;& =
)
g=
$
g#/d#;A4

10
CHƯƠNG 3
Cơ học hệ chất điểm - Vật rắn
 !"#L%&'(!"$ !*+,  /&012'-3") !
*) Môc tiªu:
)4 5'6789;&: 3 <=;& M=>,9:96I 2783A6?9@73A9&19&'(536C3A9JE;& M=/D'
2'-9&'(536C3A9JE;& M=4
$4& !2 6789.&7B3A@G3&9&'(536C3A9JE>-@m3D'E3&=C@O996V3&4& !2 6789
+ 5'&Q9W3&9P3A>,6C3A3‚3A9JE>-@m3@13A9&'(536C3AD'E(D'E3&=C@O996V3&4
L4&Q3A= 3&67896V3&2%=P=n36C3A2783A>,6V3&2'-+011,3=P=n36C3A2783A4
a4-3NO3A6V3&2%+ !3& e36C3A3‚3A65A 0 &W9&9:9+, 1:3@13A9&'(536C3AD'E(4
3.1. Khối tâm. Chuyển động của khối tâm
L4)4)4V3&3A&rE
Yk6,-6#<"!6)

;)

;;)

JM5 ? 75+6

;6

6

5+6#"!6HA"02l
   
     
6 ) H 6 ) H  6 ) H 3+ + + =
uuuur uuuuur uuuuur

L`)
[E6C9JE;& M=6 >Y =CA9[E6C3,16X"

g
v
>Y +E[E6C2,~/
”/•*

_
g

@
>Y +E[E6C2,j

/(

/‡

/E6789"
  
 
Q 6 g) m 6=
∑ ∑
ur uuuur
L`$
&E("
  
 
e 6  m 6=
∑ ∑

*
     
   
n 6  m 6 o 6  m 6= =
∑ ∑ ∑ ∑
 L`L
:96F3A&Q9L`$/L`L9&1.&k.EW3&[E6C;& M=9JE=C&<9&K6 5=4M(
A U9&}3AE;&01S:9:9W3&9&K9JE;& M=>p=?6C3A2T9&[94
L4)4$4-399JE;& M="
  
 
 6  m 6=
∑ ∑
ur ur
L`a
G/
∑
=
3
)

>=
g
∑
=
3
)

.
 gu3A6C3A2783A


9JE&</N16X>-39;& M=9&1+c "


 p m 6=
∑
ur ur
/S'(@E"

g
∑
=
3
)

= )(
4  L`d
-("@`"#5 ?,-2P"#5 ?,-6#<"!6"c&Mk6,-
;JM5 ?2P`M5 ?,-+J2PMk6,-
L4)4L4&7B3A@G3&9&'(536C3A9JE;& M=
 0& !9:99&K6 5=_
)
/_
$
444_
3
9JE&<2y32789&V':9NO3A9JE3&]3A2T9"
)
†
/

$
†
/444/
3
†
>,9&'(536C3A>Y 3&]3A>n9BA E9"
)
E
/
$
E
/444/
3
E
&\E=•39:9.&7B3A@G3&"
=
)
)
E
g
)
†
*=
$

$
E
g
$
†

*444*=
3

3
E
g
3
†
4_'3G=.&7B3A@G3&9&'(536C3A9JE;& M=/
E6I1&,=L`a&n1/E6789"
∑
=
3
)

E= )(
g
∑
=
3
)

†
 L`h
@13A6X/
E
g
N
N
2,>n9BA E99JE;& M=4Yk6,-6#!"#

6#<"!6JM5 ?2P`M5 ?,-+0A4\,-6#5U2P
`?'&5UA4\5F
3.2. Các định luật bảo toàn. Bài toán va chạm
11
L4$4)4V3&2'-+,11,36C3A2783A
D@5
 >Y =C&<9&K6 5=9&'(536C3A>,2,=C&<9P2 3A&rE2,
†
g#&G"
( )
33$$))
>=>=>=
N
N
+++
g#3A&rE2,"
33$$))
>=>=>= +++
g
913S
 L`q
@`"#5 ?,-6#Z55+6#"&5 ?2O''+G>-399&'(536C3A9JE;&
M=9JE&<"
  
 
 6  m 6
   
=
 ÷  ÷
   

∑ ∑
ur ur
/3e3>-39;& M=9JE&<9P2 "

g
const
L`s
Yk6,-6#Z5'c"7F'c!"#]"=
DHOX ?*q5K+!"#O5US 8EU"E9
3.3. Bài toán va chạm (T6[9)
&}%"E9&I=2,ST7B3A:9A ]E9:9>-@13A=C;&103A&U A E3@K3Am34@13A
&U A E3>E9&I=/9:92T97B3A:9+ !36u @K3&E3&4@7Y9>,SE'2}9>E9&I=;&P3A9X7B3A
:9A ]E9:9>-4^& A 0 9:9+, 1:3>E9&I=/3A7U E91 9:9>->E9&I=3&E'2,=C&<9P
2 />,:.NO3A9:96V3&2'-+011,36C3A3‚3A>,9B3‚3A9&19:9&U A E3@7Y9>,SE'>E
9&I=/=,;&P3A9y33A& e39Q';r9:92T97B3A:9@13A&U A E3>E9&I=4
3.4. Chuyển động của vật rắn. Phương trình cơ bản chuyển động quay của vật rắn.
L4a4)4&'(536C3A9JE>-@m3
DrI!"#0 ^& =C>-@m39&'(536C3AV3& !3=[ 9&K6 5=9JE3X
9&'(536C3A&n13&]3AD'H6I1A 3A3&E'*I =‰ &U 6 5=9:99&K6 5=9JE>-@m3V3&
 !36p'9X9l3A>n9B>-39>,>n9BA E94 0& !
E
2,>n9BA E99&'3A9JE9:99&K
6 5=_
)
/_
$
444/_

4V3&2'-n„13"
∑∑

=










†E=
L`t
L`)$2,.&7B3A@G3&9&'(536C3A9JE;& M=>-@m3/>-(='3;&01S:9&'(53
6C3AV3& !39JE=C>-@m3E9&…9y3jk9&'(536C3A9JE;& M=9JE3X4
DrI!"#-
L4a4$4&7B3A@G3&9B+039JE9&'(536C3AD'E(9JE>-@m3D'E3&=C@O996V3&
Dr_P=n39JE2T9

†
6 >Y @O9D'E(∆2,
m
j:96V3&+c "
m
g

†@Λ
L`)#
'(@E")Z6,-6#5U"L\
∆

*[2PMZM5U"J2PMZ'cM
5U"J"_]L
∆
'cMA,-5U"-\-
+A7U E9€3A&K(@o3A=P=n3
m
9JE
t
F
6 >Y @O9∆2,=P=n39JE
t
F
6 >Y
6 5=/A E16 5=9JE∆>,=?.&F3A9&QE
t
F
4
Drp 2O,-!"#-
R+ 5'&Q99JEn„13ES'(@E"
∑ ∑
=β

$

@=
m
)


L`))

&}%
∑

m

g
m
s`?6Z6A'&5\:9NO3A2e3>-@m3*
∑
= @=
$

A[ 2,6Z6AX9JE>-@m36 >Y @O9∆3X+o3Au3A9:9=P=n3D':3W3&4
-(L`)d9X&56789> !&,3&"4
m=β
 L`)$
12
D
D
,.&7B3A@G3&9B+039JE9&'(536C3AD'E(9JE>-@m3j'3AD'E3&=C@O94
DrD@X6Z66AXA7U &[9T6[99:9>WNOW3&=P=n3D':3W3&9JE=CS
@7U3A&8.6?9+ <4&}3AE9€3A9X&5Nl3A6V3&2WtuF '(An3S`n 3n@65
G==P=n3D':3W3&6 >Y =C@O9+K;G4
Drr/#N'+v,-w–
6
g

x

ω

z

6

4
*) Tài liệu học tập chương 3
)47B3A'(e3G3&)ttt/5V"& / )/&,~'K+03 :1NO9/,C 4
$47B3A'(e3G3&$##)/W+5X"& ; )/&,~'K+03 :1NO9/,C 4
*) Câu hỏi, bài tập, nội dung ôn tập và thảo luận chương 3
Câu)4^&: 3 <=>p;& M=9JE&<9&K6 5=•1S:3&9&'(536C3A9JE;& M=>Y 9&'(53
6C3AV3& !39JE>-@m3>,9&'(536C3A9JE9&K6 5=4
Câu$4&,3&.&y33,19JE2T99X:9NO3A&T9STAM(@E9&'(536C3AD'E(9JE>-@m3D'E3&
=C@O996V3&•&M3W9&I SE1•
CâuL4& !2 .&7B3A@G3&9B+039JE9&'(536C3AD'E(/3e'%3A&rE9JE9:96I 2783A
@13A9P3A&Q94
Câua4&]3A6I 2783A3,16?9@73A9&19&'(53NC3AD'E(9JE>-@m3j'3AD'E3&=C@O99
6V3&•
Câud4V3&3A&rE=P=n3D':3W3&9JE>-@m3/3e'9:9&W3&=P=n3D':3W3&9JE=CS>-
@m34 !9P3A&Q9W3&=P=n3D':3W3&9JE=C>-@m36Z3A9&KD'E(D'E3&@O96 jQ3A
>,6 D'E;& M=9JE3X4
Câuh4^&: 3 <=>p=P=n36C3A2783A>,9&Q3A= 3&9:96V3&2%>p=P=n36C3A2783A6
>Y >-@m3D'E(j'3AD'E3&=C@O996V3&4
Câuq4!'9:96I 2783A@13A9&'(536C3AD'E(9X>E @w7B3AT>Y 9:96I 2783A@13A
9&'(536C3AV3& !34T7B3AT3,(&5& <33&7&!3,1c3&]3A9P3A&Q93,14
Câus4&Q3A= 3&>,.&:+ 5'6V3&2'-+011,3=P=n36C3A2783A4&1>, >W
NOQ3ANO3A>,A 0 &W9&4V3&2'-3,(6789&10=•3@13A3&]3A6 p'; <33,1•
Bài 3.1._C@O9D'E(&G3&@O6?9+:3;W3&$#===g)##;A9X&5D'E(D'E3&
=C@O93o=3AE3A4_CS8 NM(;&P3AN•36789D'K3D'E3&@w3A@[9>,6y'T
N19JES8 NM(9X@n1=C>-3?3A;& 2783A$#;AG3&L4)4\D'E=ES:
9JE@O9D'E(/2T99039JE;&P3A;&W>,;& 2783A9JES8 NM(4K(Agt/s#xS

$
4
 E99JE>-3?3A>,2T99‚3A9JENM(@n1>-3?3A4
Bài 3.2._C&E3&3?3A&F3A9X !N <36p'>,N, #/q#=9X&5
D'E(D'E3&=C@O93o=3AE3A6 D'E=C6y'9JE&E3&4}9
6y'/&E3&6789A ]c>V@W3o=3AE3A4E'6X/3X6789&0@E65
TD'E(4K(Agt/s#=S
$
4•(j:96V3&A E9AX99JE&E3&3,(
2}9+m6y'6789&0@B >,2}96 D'E>V@W&F3A6Q3A4
Bài 3.3. _C@O6?9;& 2783A$/d#;A>,=C>-3?3A;&
2783A#/d#;A67893 >Y 3&E'+o3A=CS8 NM(;&P3AN•3>m
D'E=C@w3A@[9G3&4L4$4\D'E;& 2783A9JES8 NM(/9JE@w3A@[9>,9JE;&'3AAm3>Y
@O6?94^& &0>-3?3A653XT9&'(536C3A&G@O6?92‚3;&P3A@78@e3=?.&F3A3AE3A4
<S=ES:A ]E=?.&F3A3AE3A>,@O6?9+o3A#/)#4K(Agt/s#=xS
$
4G=A E99JE>-
>,2T99‚3A9JES8 NM(4
13
CHƯƠNG 4
Trường lực thế và Trường hấp dẫn
 !"#$%&'(!") !*+,  /&012'-3") !
*) Môc tiªu:
)4  5';&: 3 <=>,W3&9&K9JE@7U3A2T9&!/ @7U3A2T9&K.N‹3/&!3‚3A>,9B3‚3A
@13A@7U3A2T9&!4B6Z&!3‚3A>,6V3&2'->I3>-&K.N‹34:96V3&2'-^n.2n@
$4  !>-3NO3A9:9; !3&Q9653A& e39Q'9&'(536C3A@13A@7U3A&K.N‹39JED'06K/
G=67899:9>-39>€@O4
L4  5'9:96V3&2'-^n.2n@4
4.1. Khái niệm và tính chất của trường lực thế
_C9&K6 5=6789A[ 2,9&'(536C3A@13A=C 85U3!'I =‰ >V@W9JE9&K

6 5=  6p'  j'K  & <3  2T9 
b
 :9  NO3A  2e3  9&K  6 5=  K(4 !'  9P3A  f
_
 9JE  2T9 
†
 2,
∫
=
_
_
NS†f .
/;&P3A.&O&'C967U3ANV9&9&'(53_=,9&….&O&'C9>V@W9JE6 5=6y'
_>,6 5=9' &GE3X @o3A"
)(@†
2,2T99JE6# 85U
&WNO>p@7U3A2T9&!" @7U3A@[3A2T92,=C@7U3A2T9&!*@7U3Ar3&6 <3'2P3A2,=C
@7U3A&!T9&Q3A= 3&4
4.2. Thế năng trong trường lực thế
a4$4)4V3&3A&rE&!3‚3A" @N,-<"!6' 85U5+6#+6y

\
#0X,-<"!6*-''f
_
g–

_`–

4 a`)
&WNO"&!3‚3A@7U3A@[3A2T9>,&!3‚3A@7U3Ar3&6 <3'2P3A4

a4$4$4W3&9&K&!3‚3A
E&!3‚3AI =C>V@W6789j:96V3&SE ;&:9=C&o3AS9C3A3&73A& <'&!3‚3A
A ]E&E >V@W&G&1,31,3j:96V3&4
+ ]E@7U3A2T9>,&!3‚3A9X&<&Q9SE'"
∫
−==
_
_
–_–NS†f )()(.
a`$
4.3. Cơ năng
@`"#N+N,-<"!6–g–
6
z–

" ?E5+N,-<
"!6Y<"!6!"#'6# 85U=,;&P3A9&V':9NO3A=C2T93,1
;&:9N,-<"!65+6#"&5 ?2O''+S"052O''+N'
 85U9
4.4. Trường hấp dẫn
a4a4)4V3&2'->I3>-&K.N‹3
H--<"!62<MJM5 ?6

;6

"cA-6#M'O;J
5U<4{-
)$
†
;+

$)
†
 LB<"!6+"<"!6M-; 8"#,-5Uj5
LXM5 ?-<"!6+j50L2 M'OA-q4

)$
†
g`
)$
L
$)
@
@
==

a`L
@13A6Xj:96V3&+o3A&T93A& <="gh/hq$#
±
#/##a)=
$
x;A
$
4
a4a4$4^&: 3 <=@7U3A2T9&K.N‹3
K9Q=C>-3,19€3AAM(@Ej'3AD'E3&3X=C@7U3A&K.N‹34@7U3A3,(2,=C
NI3A6?9+ <9JE>-9&K4X 9:9&;&:9ST9X=?9JE=C>-6•2,=+ !36u W3&9&K9JE
14
rI!"#,-
' 8E5U
;&P3AA E3j'3AD'E3&3X4@7U3A&K.N‹3N1=‰ >-AM(@EZ3I 6C92 /;&P3A2<&'C9>,1

ST9X=?9JE9:9>-;&:94
a4a4L47U3A6C@7U3A&K.N‹3"
)
)$
=
†
g
A
g
)$
L
)$
$
@
@
=
−
4A6?9@73A9&1;&03‚3A&K.N‹39JE>-=
$
I 6 5=;&01S:4
I 2783A>n9B
A
3,(A[ 2, 8"# 8<4{9JE>-=
$
I 6 5=;&01S:4
a4a4a4@7U3A&K.N‹39JE@: 6K
@7U3A&K.N‹39JE@: 6K;& 2783A_6789A[ 2,@7U3A@[3A2T9&E(@[3A@7U3A4
 E9@[3A@7U3A@e3=?6K"
3


H)

Q
=
/A E9@[3A@7U3AAc6C9E1&"

H)

S Q  9
=
+
4 a`a
4.5. Chuyển động trong trường hấp dẫn. Các định luật Kepler
a4d4)4&'(536C3A@13A@7U3A&K.N‹33&79:9& e3&5/9:9>< 3&3&M3I14442,9&'(536C3A
@13A@7U3A2T9&!j'(e3M=4 0 9:9+, 1:33,(E&'67899:9;!D'0"D'H6I19JE=C>-
2,=C !N <3P3 9n2 ./.E@E+12/&E(&(.n+12l(&'C9>,16 p'; <3+E36y'4!':.NO3A
9&1@7U3A&8.&,3& 3&9&'(536C3AD'E3&=?@U &G@}@E
6789+E6V3&2'-=,^n.2n@6•jM(NT3ARS2 <'D'E3S:/9O
&53&7SE'"
-9 $%"&',-+5+6#56+6c8l&6#
'-F"!6
29 WAMX&B6c8"+C4
X2P-'M'O8-2P-
9 W M!"#,-+j5L5%
B-22-,-2A\5L%"&'
a4d4$4&'(536C3A@13A@7U3A&K.N‹39JED'06K
!'R=C6 5=f3,16X@13A@7U3A&K.N‹39JED'06K/E+m36 =C> e36I3;&
2783A=>Y >-396y'2,>
#
&G2W&'(!>,&T93A& <=9&Q3A\@o3Al(&n1@VS9JE>

#
9X
&5j0(@E=C@13A3&]3A@7U3A&8.SE'" e36I3@B @c>pD'06K*&1?9> e36I3+E(>w3A
D'E3&D'06K&n1=CD'H6I1;W3@w3&E(n2 .*&1?9> e36I3+E(3A,(9,3AjED'06K4
@VS>-39+E36y'>
#
9y3& !65+m3> e36I3+E(>w3AD'E3&D'06K&n1=CD'H
6I1@w3A[ 2,^\<
@VS & 5'9JE>-39+E36y'>
#
9y3& !65+m3> e36I3+E(3A,(9,3AjED'06K
A[ 2,^\<xx
ri@X^\<x
EW3&>-39>
)
;& > e36I39&'(536C3A@w3j'3AD'E3&D'06K4 0& !> e36I3
+E(9:9&=?6K;&P3AjE2m=65E9X&591 +:3;W3&D'H6I19JE3X+o3A+:3;W3&v9JED'0
6K4-39>

9JE> e36I3@13A9&'(536C3A@w39X2 e3&<>Y A E9&7Y3AM=/2,A E9
@[3A@7U3A

3


Q
=
R6XS'(@E"
vA>
#

=
gq/t;=xS
;
s;=xS a`d
15
!'+m3>Y >-396y'>
#
|s;=xS> e36I3S—@B @c>pD'06K/3!'+m3>Y >-396y'
>
#
{s;=xS3&73A3&\&B3>

&G> e36I39&'(536C3Aj'3AD'E3&D'06K&n1D'H6I1n2 .4
ri@X^\<xx
 0Sƒ> e36I3j'K.&:Rf9:9&M=9JED'06K=C;&103A+o3A+:3;W3&D'06K
v/>Y >-396y'>
#
>,+E(3A,(9,3AjED'06K6!3
∞
:.NO3A6V3&2'-+011,39B3‚3AE
6789"
vA$>
##
≥
>-(/>-39>€@O9K."
vA$
#
=
g))/$;=xS  a`h
*) Tài liệu học tập chương 4

)47B3A'(e3G3&)ttt/5V"& / )/&,~'K+03 :1NO9/,C 4
$47B3A'(e3G3&$##)/W+5X"& ; )/&,~'K+03 :1NO9/,C 4
*) Câu hỏi, bài tập và đề tài thảo luận chương 4
Câu)4&:+ 5'6V3&2'-&K.N‹3>€@O4G=+ 5'&Q9A E9A9JE=C>-.&O&'C9>,16C
9E1&S1>Y =?6K4
Câu$4e'>, Q3ANO3A9JE6V3&2'-&K.N‹3>€@OW3&;& 2783A9JED'06K/=?@U 444
CâuL4&'(536C3A9JE>-6 >Y @: K4Œ3A&rE>,+ 5'&Q996C>€@O9K.>,9K.4
Bµi 4.1._C.& 9P3A2: =C=:(+E(&T9& <3=C>w3A3&,12C39X+:3;W3&$##=@13A=?
.&F3A&F3A6Q3A4^& 2783A9JE.& 9P3A+o3Aqd;A4K(A E9@[3A@7U3AAgt/s#=xS
$
4
•(j:96V3&"
E4T93k39JE.& 9P3A:9NO3A2e3A&!3AZ I 6 5=&K.3&K>,6 5=9E13&K9JE>w3A
3&,12C3;& >-399JE=:(+E(@13A>w3A3&,12C32'P3;&P3A6u >,+o3ALh#;=x&4
+4Y >-393,19JE=:(+E(;& &T9& <3>w3A3&,12C3/3A7U .& 9P3A+m6y'+V@B ;&\
A&!3AZ •
Bài 4.2._C>-@B TN1R6C9E1&g)t/h=4&1Ag)#=xS
$
4
E4W3&&U A E365>-@B &!6C9E16X4
+4W3&D'•3A67U3A=,>-6 6789@13A#/)A M(6y'>,@13A#/)A M(9' 9l3A4W3&&U A E3
65>-@B 6789)=6y' e3>,)=9' 9l3A9JED'•3A67U3A4\D'E=ES:9JE;&P3A;&W4
Bài4.3. R6C9E1&g$/)=/3A7U E3k==C&w36:2e39E1>Y >-39+E36y'>
1
3A& e3A=C
AX9’gad
1
S1>Y .&7B3A3AE3A4w36:6I6789y=+E(jE2ga$=4W3&"-39+E36y'9JE
&w36:/&U A E3&w36:9&'(536C3A@13A;&P3AA E3/®C9E19T96I =,&w36:6I67894
16

i|4a
CHƯƠNG 5
Cơ học chất lưu
 !"#$%&'(!") !*+,  /&012'-3") !
*) Mục tiêu:
)4  5'&!3,12,9&K27'>,9&K27'2W7c3A/.&7B3A@G3&2 e3O94
$4 -3NO3A6789.&7B3A@G3&n93'2 n@31'22 >,Q3ANO3A/>-3NO3A.&7B3A@G3&3,(65
A 0 =CS+,  >p9&K27'4
L4  <3783A3C =ES:3&Y>,6V3&2'-n„134
5.1. Chuyển động của chất lưu lí tưởng. Phương trình liên tục. Dòng chảy tầng và dòng
chảy rối. Số Reynolds
d4)4)4&'(536C3A9JE9&K27'2W7c3A
&K27'+E1AZ=9:99&K2\3A>,9:99&K;&W4p=?9B&[9/=C9&K27'9X&5D'E3
3 <=2,=C=P @7U3A2 e3O9I1&,3&+c 9:99&K6 5=2 e3;!>Y 3&E'+o3A3&]3A3C
2T97B3A:93X 9&'3A6X2,9:92T9&}4:99&K27'9X3&]3AW3&9&Ku3AD':SE'"
`&}3A;&P3A9X&G3&NI3A3&K6V3&3&7=C>-@m34
`:99&K27'+E1AZ=9:99&K27'N˜3k39&K;&W>,9:99&K27';&X3k39&K2\3A4
`^& =C9&K27'9&'(536C3A/9:92Y.9JE3X9&'(536C3A>Y 3&]3A>-39;&:9
3&E'/3e3A ]E9&}3A9X3&]3A2T97B3A:9A[ 2,5U#6-*A&E(5UL3!'9X$2Y.
9&K27'9&'(536C3A>Y 3&]3A>-392y3278+o3A>
)
>,>
$
>,A 0Sƒ>
)
{>
$
/;& 6X2T93C =E
S::9NO3A2e32Y.9&K27'>-39>
)

3A7899& p'9&'(536C3A>,:9NO3A2e32Y.9&K27'
>-39>
$
9l3A9& p'9&'(536C3A4
I<5 5X l&K27'&1,31,3;&P3A3k36789>,@13A9&KK(;&P3A9X9:9
2T93&Y4_C9&K27';&P3A2%7c3AA[ 2,=C<5 U-(/=[ 9&K27'6p'2,9:9
9&K27'&T94'(3& e3=C9&K2\3A@K27'6C3A;&P3A3&Y9X&5I=91 3&7=C9&K
27'2W7c3A4
A1, @E/&n1@e3/2T93C =ES:9&…j'K& <3@13A9&K27'9&'(536C3A/>-(=C9&K
27'c@I3A&: 3o=(e39XAy36y(6J9:9W3&9&K9JE=C9&K27'2W7c3A4
&T93A& <=9&1&K(9&'(536C3A9JE9&K27'2W7c3A9X3&]3AW3&9&KSE'"
)4 &K27'@K2 3&6C3A/& 5'=C9:9&&P3A&7U3A2,9&K4}O3A&rE2,2Y.3,(@78
@e32Y.;&:9&y'3&7;&P3A9X=ES:4E3X 9&K27'MZJ5U24&"+_ ?4
$4&K27'jJ5U24&"+_!X3A&rE2,9X2T96,3&Z j'K& <3;& 9&K
27'+V3k3&E(A •3R=[ .&WE4
d4)4$4&7B3A@G3&2 e3O9
!'

9&….&O&'C9>V@W_=,;&P3A.&O&'C9E3X <5 !"#4B
@13A9&7B3A3,(E9&…jk9&'(536C3ANR3A9JE9&K27'4
b'H6I19JE9:99&K6 5=9JE9&K27'9&'(536C3A
6789A[ 2,9:9" 84a/6X2,3&]3A67U3A913A=, !.
'(!3I =‰ 6 5=9X.&7B3A@l3A>Y .&7B3A9JE>n9B
>-399JE9&K6 5=9JE9&K27'I 6 5=K(4:967U3A
Nw3ATE@e3=C67U3A913A;W3I1&,3&=C4a4
~k9&K27'9&'(536C3A@13A=C3ANw3A@K
3&\"A[ 
)

∆

>,
$

∆
2, !N <3&F3A+K;Š9JE3ANw3A
K("
$$))
>> ∆=∆
4 d`)
17
i
d4)4L4w3A9&0(y3A>,Nw3A9&0(@ 4vn(312NS
A& e39Q'9&'(536C3Au3AD':9JE9&K27'vn(312NS6•G=&K(W3&9&K9JENw3A
9&0(.&O&'C9>,1A :@V9JE=C6I 2783A;&P3A&Q3A'(e3"v
n
g
η
ρ
>
A[ 2,Svn(312NSv
n
4
@13A6X2,"&5 ?"c ,-/3X9X&52,6CN, /9X&52,67U3A;W3&3A444/>2,
>-397B3A6 9JE9&K27'&1?9>-399JE>-9&'(536C3A@13A9&K27'/η2,6C3&Y4
^!D'0"v
n
|$L##9&K27'9&0(&,3&2Y./v
n
{$L##9&K27'9&0(9'C3j1:(/v
n


≈
$L##9&!6C9&0(&,3&2Y.+m6y'+V.&:>™/AM(9&K36C3A3e3&,3&3A4
&7>-(Svn(312NS9&1E3&]3A9&… e'D'E3@[3A>pW3&9&K9&'(536C3A9JE9&K
27'4X6789>-3NO3A@13AST3A& e39Q'=P&G3&9:9=:(+E(/,'&'š/,'3Ay=444G=6 p'
; <3 7'@13A;r&'-N‹3Ny'/;&W&n167U3A3A4
5.2. Phương trình Becnuli (Bernoulli) và ứng dụng
d4$4)4&7B3A@G3&n93'2 
 ~k=C;& 9&K27'f9&'(536C3A@13A=C3A
Nw3A3&\A Y &I3+c &E  !N <3fg
)
∆
>,g
$
∆
N7Y :9NO3A9JE@[3A@7U3A6p'9JED'06KA[ >
)
>,>
$
2y3
2782,>-399&K27'I f>,/‡
2
>,‡
$
2,9:96C9E1
9JE$>V@Wf>,/E6789"
)
$
))$
$

$$
A•>
$
)
A•>
$
)

ρ+ρ+=ρ+ρ+

E("
A‡>
$
)

$
ρ+ρ+
g&o3AS",.&7B3A@G3&n93'2 d`$
d4$4$4<D'09JE.&7B3A@G3&n93'2
i@ 8?<5 O'6#P6-

s


2
>,
$
27'2783A9&K27'@13A3A;&P3A6u >,+o3A"bg>
)


)
g>
$

$
4
&7B3A@G3&@e39X&5> !
$
$
$
$
$
)
$
)

b
$
)


b
$
)
 ρ+=ρ+
4 d`L
!'
2

≥


$
R.&7B3A@G3&@e3@}@E
2

≥

$
4-(;& 9&K27'9&'(536C3A@13A=C
3A3o=3AE3A9X !N <3&E(6u &G9~+'45L;A*<^5L+?5&
 ?4
iIZ7@Z5S@'559
_C+G3&6:(@C3A9&QE=C9&K2\3A*Ay36:(+G3&9X=C2‰3&\/I 6X9X=CNw3A
9&K2\3A9&0(@E4I =C&U 6 5=A[ &2,6C9E19JE9&K2\3A@13A+G3&/E:.NO3A
.&7B3A@G3&n93'2 9&1$>V@W"f@e3=?9&K2\3A>,I 9&‰9&K2\3A9&0(@E4
E9X"

$
f
A‡>
$
)
A‡ ρ+ρ=ρ
>Y >g>

>,&g‡
f
`‡

4

-(/>-399&0(@E9JE9&K2\3A"
A&$>
$
=
 d`a
5.3. Hiện tượng nội ma sát (nhớt) và định luật Newton
d4L4)4 <3783A3C =ES:>,6V3&2'-n„13
 0Sƒ9X=CNw3A9&K27'9&'(536C3A/A ]E&E 2Y.9&K27'9X2T97B3A:9"2Y.
9&'(536C3A3&E3&;k12Y.9&'(536C3A9&-=/2Y.9&'(536C3A9&-=3A‚39032Y.9&'(53
6C3A3&E3&4 <3783A6XA[ 2,& <3783A3C =ES:2T93&Y"2T93,(3o=&n1.&7B3A
18
iD
ir
 !.'(!39JE=? !.j}9A ]E&E 2Y.;&W4&T93A& <=9&Q3A\@o3A2T93C =ES:A ]E&E
2Y.9&K27'>'P3AAX9>Y ‡9X97U3A6C…2<>Y 6C+ !3& e39JE>-396V3&&7Y3A'&n1
.&7B3A‡>,…2<>Y N <3W9& !.j}9
u
∆
A ]E&E 2Y.;&W"

N‡
N'
†
∆η=∆
4  d`d
η2,=C&<S…2<A[ 2,&<S3C =ES:&E(&<S3&Y4P3A&Q9d`dA[ 2,6V3&
2'-n„134@13A&<6B3> /&<S3C =ES:
η
W3&@ESx=
$

g;Ax=S4
d4L4$4P3A&Q994
 0Sƒ9X=CD'09y'3&\+:3;W3&@9&'(536C3AV3&
 !3>Y >-39'@13A=C;& 9&K27'419X& <3783A
3C =ES:/D'09y'2P ;k1=C2Y.9&K27'cAy3=?9JE3X
9&'(536C3A&n14&T93A& <=9&Q3A\@o3A+pN,(9JE2Y.
9&K27'3,(>,1;&103A

L
$
*.&M3ƒ9&K27'c3AE(S:=?
9y'9X>-396V3&&7Y3A'*6 >Y 9:9.&M3ƒjE&B3/>-39K(A 0=Ny3
>,6!3;&103A9:9&
@
L
$
>-39K(+o3A#4-(9X&5W3&6C+ !3& e39JE'
&n1‡"
# L
$ x L $
4  
4  
−
= =
4T93C =ES:+o3A2T9903:9NO3A2e3D'09y'
6789W3&3&7SE' "
$
@a
@
'

$
L

N‡
N'
† πη=∆η= .
g
h 
πη
4 d`h
[ 2,9P3A&Q994X6}3A6 >Y 3&]3AA :@V9JE>-39';&P3A2Y32m=4
*) Tài liệu học tập chương 5
)47B3A'(e3G3&)ttt/5V"& / )/&,~'K+03 :1NO9/,C 4
$47B3A'(e3G3&$##)/W+5X"& ; )/&,~'K+03 :1NO9/,C 4
*) Câu hỏi, bài tập và đề tài thảo luận chương 5
Câu)4 V3&3A&rE>p:.S'K9JE9&K27'4 >Y 9&K27'6Q3A(e3/9&Q3A\@o3A:.S'K
&n1=[ .&7B3A2,3&73&E'4
Câu$4^&: 3 <=67U3ANw3A>,3ANw3A4V3&2%>pW3&2 e3O99JE9&K27'4
CâuL4&7B3A@G3&n@31'22 4&7B3A@G3&9M3+o3A9JE9&K27'4T96›(f@9& =nNn4
Câua4T93&Y@13A9&K27'4T99034
19
CHƯƠNG 6
Dao động và Sóng cơ
 !"#$%&'(!"$ !*+,  /&012'-3"# !
*) Mục tiêu:
)4 5'>,.&M321I 67899:921I NE16C3A9B/SX3A9B&[9>,STA E1&1E9JESX3A9B&[94
$4 0 &W9&67899:9& <3783A>pNE16C3A>,SX3A9B@13AT3& e34
L4 5';&: 3 <=SX3AM=>,9:96?9@73A>I2%>,S 3&2W9JEM=4
6.1. Dao động
.p 4-'"#"=a-

 !+ 5'&Q96V3&2'-n„136 >Y D'09y'>,+ !36u E6789"
$
$
N
jN
z
#j
$
#
=ω
>Y  ω#{#/3A& <=9JE3X9XNI3A"jgf91Sω#zϕ h`$
-39>,A E99JE9132m92w21NE16C33A6 p'&wE"
>g
N
Nj
gEω
#
S 3ω
#
zϕ*Eg
N
N>
g`E
$
#
ω
91Sω#zϕ&E("Eg`
$
#
ω

4j
.TN5 ?4-'"#"=a-
B3‚3A4-'"#"=a-9&1+c "–g–
6
z–

g
$
)
;f
$
h`L
–
6
g
$
)
=>
$
g
$
)
=f
$
4
$
#
ω
4S 3
$

ω
#
zϕ*–g
$
;j
;jNj†Nj
$
j
#
j
#
−=−=
∫∫
 h`a
h4)4$4E16C3A9BmNy3
.p 4-'"#w4v
u3A&8.2T9:9NO3A2e3D'09y'2,"†z†
9
g`;j`@>
&7B3A@G3&> .&M39JENE16C3AmNy3"
#j
N
Nj
$
N
jN
$
#

$

=ω+β+
4•6X"
$
#
=
;
ω=
>,
$ 4

6
β
=
&n1A 0 W9&/;& ω
#
{β3A& <=9JE3X9XNI3A"
91Snfj

#
ϕ+ω=
β−
h`d
M(9&W3&2,.&7B3A@G3&NE16C3AmNy34o3ASω2,y3SAX99JENE16C3Am
Ny3"
$$
#
β−ω=ω
416X9&';G9JENE16C3AmNy32,"
 
3

 
@
π π
ω
ω β
= =
−
 h`h
.YO'*A4-'"#w4v
fgf
#
n
`
β

2,+ e36C9JENE16C3AmNy3*@œ@,3A3XA 0=&n1&U A E3&n1D'(2'-
&,==€*>G@o3A"`)|91Sωzϕ|)/3e3`f
#
n
β

||j
≤
f
#
n
β

4p=?2W&'(!=,3X ;& 
g∞&G+ e36CfA 0=6!3;&P3A4&73A&T9!9&…SE'=C&U A E36J2Y3/+ e36CA 0=Ny3

6!3=C@VS;&P3A91 3&7+o3A;&P3A4 0=2783A2PAE9X@VS+o3A2PAET3& e39JE…S
A ]E&E @VS2 e3 !.9JE+ e36CNE16C3A9:9&3&E'=C;&103A&U A E3+o3A=C9&';G"
δ
23
@

β
=
gβ  h`q
1S:3&9&';G9JENE16C3AmNy3>Y 9&';G
#
9JENE16C3A@ e3A6 p'&wE/E&K(/
{
#
4M4-'"#w4v5LMF9JENE16C3A6 p'&1,9JE&<4
.D•-'"# €27
20
-/01-•-'"#6+U4 LA4\,-'&5Uv'+E5+4-'
"# €27/NE16C3A97™3A+Q99X9&';G+o3A9&';G9JE3A1I 2T9'y3&1,3:9NO3A4
2p 4-'"# €27T9:9NO3A2e3D'09y'AZ=2T9;k1>p†g;j>,2T9
903†
9
g`@>>,3A1I 2T9'y3&1,3"
F
g491SΩ/9&';Š"
Ω
π
=τ
$
h`s

&7B3A@G3&n„139&1D'09y'"=Eg`;j`@>z91SΩ
'(@E"

=

j
N
Nj
$
N
jN
$
#
$
$
Ω=ω+β+
cos
 h`t
A& <=9JE.&7B3A@G3&> .&M33,(2,"jgf91SΩzΦ/@13A6X9:9&o3ASf>,Φ
6789W3&&n19:99P3A&Q9"
( )
$$
$
$
#
$
a=

f
Ωβ+ω−Ω

=
/
$
#
$
$
A
ω−Ω
β
−=Φ
h`)#
>Y 6 p'; <3
#$
$$
#
>β−ω

YO'*A4-'"# €27I# l
@7Y9&!/E&K(@o3A+ e36Cf>,.&E+E36y'Φ9JENE16C3A97™3A+Q96p'.&O
&'C9y3SAX99JE3A1I 2T9:9NO3A4A& e39Q'ST.&O&'C99JE+ e36Cf&n1Ω/E6789
;!D'0SE'"
$$
#9&
$
β−ω=Ω
&G+ e36CNE16C3A97™3A+Q96I@VS9T96I 4…S9T96I 6X
W3&@E+o3A"
$$
#
=$


f
β−ωβ
=
max
  h`))
h4)4L4u3A&8.>,.&M3W9&NE16C3A
.DW!4}4-'"#"='+2P-S@U"E9
.D@`?-4-'"#"='+K +Kv*J
u3A&8.$NE16C3A"
) ) )
91S  - 
ω ϕ
= +
>,
$ $ $
91S  - 
ω ϕ
= +
E6789NE16C3Au3A
&8."
91S 4 - 
ω ϕ
= +
 Y "
)cos(
)$$)
$
$
$

)
EE$EEE
ϕ−ϕ++=
>, 
$EE
EE
A
$))
$$))
ϕ+ϕ
ϕ+ϕ
=ϕ
coscos
sinsin
4
`!'ϕ
$
`ϕ
)
g$;π&E NE16C3A&,3&.&y36789A[ 2,6Z3A.&E&G+ e36CNE16C3A
u3A&8.E6IA :@V9T96I "E
=Ej
gE
)
zE
$
`!'ϕ
$
`ϕ
)

g$;z)π&E NE16C3A&,3&.&y36789A[ 2,3A&V9&.&E&G+ e36CNE1
6C3Au3A&8.E6IA :@V9T9 5'"E
= 3
g
$)
EE −
*2}93,(j
)
>,j
$
2'P33A789NK'
`@13A@7U3A&8.u3AD':"
$)$)
EEEEE +≤≤−
.DD@`?-4-'"#"='+K +MAv*J ?A
 0SƒE9X&E NE16C3A6 p'&1,9l3A.&7B3A/;&:9y3SAX9"j
)
gE
)
91Sω
)
zϕ
)
>,
j
$
gE
$
91Sω
$

zϕ
$
4&Q3A= 3&6789@o3A@13A@7U3A&8.3,(NE16C3Au3A&8.j;&P3A
.&0 2,=CNE16C3A6 p'&1,/+ e36C9JE3X;&P3A.&0 2,=C&o3AS=,+ !3& e3>Y &U
A E3&n19P3A&Q9"
[ ]
)()(cos
$)$)$)
$
$
$
)
EE$EEE
ϕ−ϕ+ω−ω++=
 h`)$
?9+ </3!'E
2
gE
$
>,ω
)
≈ω
$
&GNTE>,19P3A&Q9h`h$>,NTE>,1.&7B3A.&:.
>n9BD'E(ES—& !2 6789NI3ASE'6M(9JENE16C3Au3A&8.j"
21







ϕ+
ω+ωω−ω
= t
2
cos.t.
2
)(
cosa2x
1212
1
h`)L
X=2I "M`?-4-'"#"='+K ;K2F"#+v*J
MA-<X-*[" ?6#4-'"#MZ"='+;J2F"#2"`6'8
-Lv*2Pv*,--4-'"#+v/J5+ ?A4 <3
783A3,(9X3& p'Q3ANO3A@13A;r&'-/6?9+ <2,;r&'->P'(!36 <34
6.2. Sóng cơ
h4$4)4:9;&: 3 <==c6y'
T4-'"#5-='6Z 8"+_" ?E5+*J"+_-
Ew5+*JX3A9B;&P3A&5@'(p3@13A9&M3;&P3A>G@13A6X;&P3A9X=P @7U3A
6,3&Z 4X3A9BAZ=*J-+*J4E
h4$4$4:96?9@73A9JESX3A4
.*J",D'•3A67U3A=,SX3A@'(p36789SE'=C6B3>V&U A E34
.&';G>,y3Sυ9JESX3A2,9&';G>,y3S9JE9:9.&y3ƒNE16C
.DW L*J
ν
==λ
v
vT

4
h4$4L4,=SX3A
#
91S 4

 ( 

ω φ
 
 
= − +
 ÷
 
 
 
&7U3A9&[3Φ
#
g#/N16X"
)
v
y
tcos(Au
−=
"6789A[ 2,
&,=SX3A4A7U E9X&5+ 5'N ˜3'N7Y NI3AS.&Q9"
)(
λ
π−ω−
=
(

$
fn'
 h`)a
>Y 9:9&& 5''9&…2,.&y3&T99JES.&Q96X4!'A[ 
3
2,>n9B6B3>V9&1+ !9& p'@'(p3
SX3A&G"
3
$
; .
λ
π
=
2,>n9BSX3A>,E9X
rk
y
=
λ
π$
>Y 
r
2,+:3;W3&>n9B>—Y 6 5==,E
;&01S:NE16C3A4&G"
)( @;
fn'
−ω−
=
h`)d
&-3jk"˜N,3A&K(@o3A'zg'*'(zλg'(/3e39:9SX3A+ 5'N ˜3D'E
A :@V9JE'@13A3&]3A+ 5'&Q9c@e39XW3&9&K'y3&1,3&n190&U A E3>Y 9&';Gg

ω
π
$
>,;&P3AA E3>Y +7Y9SX3A
λ
g>"
h4$4a4‚3A2783ASX3A9B
^& =C.&y3ƒ9JE=P @7U3A+V;W9&6C3A/3X3&-367893‚3A2783AR3A'Z3SX3A4
E16C3A6789@'(p36 /I1&,3&SX3A&G3‚3A2783A3,(6789@'(p36 @13A=P @7U3A4E
&•(G=+ 5'&Q99JE3‚3A2783ASX3A4
.rTN5 ?*J
&Q3A= 3&6789@o3A3‚3A2783ASX3A@13A.&y3&5W9&3&\δ6X6789W3&&n1+ 5'&Q9"
)
y2
t(sinaVW
222
λ
π
−ωρωδ=δ
4A&rE2,3Xj5L!X"J;LM5 ?F,-6Z
 8;L2 ,-v*+,-2F"#*J‚3A2783A9JESX3A9€3A9XW3&9&K
'y3&1,3&n1&U A E3>,;&P3AA E3>Y 9:99&';G>,λ4
22
-2
. ?}&*J
.r)"#N5 ?*J_-6C3‚3A2783ASX3A„2,.&y33‚3A2783A9X@13A=C
&5W9&9JE=P @7U3A"

($
S 3E


–
„
$$$
λ
π
−ωρω=
δ
δ
=
 h`)h
GA :@V@'3A+G3&9JE

($
S 3
$
λ
π
−ω
@13A=C9&';G+o3A
$
)
3e3=-6C3‚3A2783A@'3A
+G3&9JESX3A+o3A"
$$
E
$
)
„
ρω=

 h`)q
.rDTNZ*J
 TNZ*Jp-6#6c+'"J'6Z 85+6#"&5 ?=0*
2PN5 ?*J•-6c"J'6#"08-
 :@V@'3A+G3&@13A=C9&';G9JE3‚3A&P3ASX3A+o3A"
 

p - u

ρω
=
 h`)s
h4$4d4TA E1&1ESX3A>,X3ANR3AA7U &[9T6[9
h4$4h4A'(e32W'(A&n3>,& <3783A3& ˜'jISX3A9B
..TF5X
T*JB_g=-'+6cMXu;2-'-_g;JX<
*J6+-*[
-  2P    _  \
X?kF6cu
IA_\+" ?E5+
A_7<
..T}&*J
 0  Sƒ  =C  SX3A  .&F3A
@'(p3  @13A  =C  =P  @7U3A
6Z3A9&K>,6F3A&7Y3A4@e3
.&7B3A@'(p3/SX3A.&F3A3,(A?.=C9&7Y3A3AI >-2,=C>:9&3A‚3f4@e3>:9&3A‚39X
=C2‰3&\E/;W9&&7Y92Y3&B3+7Y9SX3A
λ
9JESX3A.&F3A4_?.&F3A6y' e3ˆ;& Y
>:9&3A‚3&G.&03jI4w39:96 5=@e32‰E/&n13A'(e32W'(A&n3/9&}3A@c&,3&3&]3A

3A'Z3&Q9K..&:@ESX3A&Q9K.4E1&G3&9JE9:9=?SX3A&Q9K.3,(9&W3&2,3A'Z3SX3A
.&:6 R2‰E4 ?A-*J"` =M"-A L&E5+
 ?}j&*J
!';W9&&7Y99JE2‰3&\&B3+7Y9SX3A9JESX3A.&F3AY /&G2‰3&\678991 3&7
=C3A'Z3.&ON'(3&K>,.&:@ESX3A9y'G3&h4)+4
..D•-'"#k6+*Jk6
-YA66l"vuJk6;A[ m2,k62,SX3A9B9X+ e36C3&\=,&W3&A :99JEE9X
&5&-3+ !67894&]3ANE16C3AM=9Xy3SNE16C3A@13A;&103AR$#‡6!3$####
‡4&]3ANE16C3A9B9Xy3SN7Y $#‡A[ 2,&IM=/@e3$####‡A[ 2,*Fk64
p.&7B3AN <3>-2W/M=3A&n6789&E(;&P3A3A&n67899&…;&:93&E'>p.&7B3A
N <3S 3&2W/&W9&&8.&1?9;&P3A6 >Y E E4
A7U E9&Q3A= 3&6789+o3A+ 5'&Q9@o3A"^&W9,3A3&•/>-39@'(p3M=@13A
9&K;&W6X9,3A2Y34&WNO/9l3Ac)d
#
/@13A;&P3A;&W>-39@'(p3M=2,La#=xS/9w3
@13A;&W
$
2,)$##=xS4@13A9&K;&W/>-39@'(p3M=>6789W3&+o3A9P3A&Q9"
23
>g
µ
γv
 h`)t
2IA"cX*5X,-k6&U&W3&A :9/9133A7U 9X&5.&M3+ <6789+E6?9W3&2%9JE
M="6C9E1/M=Sm9>,6C14
‚9/#-',-k6y3S9,3A2Y3/M=9,3A9E14&WNOM=E
L
9Xy3SaLd‡/;& ‚3A
2e3=C+:6C&Gy3SP9€3A‚3AAK.6P &,3&sq#‡4
‚9ƒ6*wž=Sm99JEM=6?9@73A9&1Sm9&: 9JEM=/3X9&1E+ !M=2,&E3&&E(

@Ÿ/@13A&E(6O9/N'N7B3A&E(&P;<9&4
_C3&I99O/;& .&:2e3/3A1, M=9B+039w39X9:9&1IM=9X:9NO3AD'(!6V3&M=
Sm99JEM=.&Q9I.>,A }.E.&M3+ <67899:93A'Z3.&:M=4
‚9/#',-k6?9@73A9&16C=I3&9JEM=
`7U3A6CM=6?9@73A9&16C=I3&9JEM=>p.&7B3AN <3>-2W4X9X@VS+o3A
=-6C3‚3A&P3A@'3A+G3&9JEM="
$$
E>
$
)
 ωρ== P
4
E&K(97U3A6CM=…2<>Y +G3&.&7B3A+ e36CM=E
$
4 e36CM=9,3A2Y3/M=
9,3A=I3&4B3>V9JE97U3A6CM=6C2, x=
$
4S&E(–x=
$
4
`C19JEM=6?9@73A9&16C=I3&9JEM=>p.&7B3AN <3S 3&2W4GE 3A7U 9&…
3A&n67893&]3AM=9Xy3SR$#‡6!3$####‡3e36C19JEM=9&…9X%3A&rE@13A
;&103Ay3S6X4e+n&eS3n6•G=67896V3&2'-j:96V3&6C19JEM=@n19P3A&Q9"
g;421A
0I
I
@13A6X2,97U3A6C9JEM==,E='3j:96V3&6C1
#
g)#
`)$

–x=
$
2,
97U3A6C9BSc/;2,&<S…2<4!'61+o3A6B3>Vn3&G;g)4
..r7/Z5S•'559
[ '2,>-399&'(536C3A9JE3A'Z3M=f/'i2,>-399&'(536C3A9JE=:(&'
>,
ν
2,>-39@'(p3M=/E&'6789;!D'0"
ν
−
+
=ν .
'
'
'>
'>
4-(/@13A@7U3A&8._k6
+6A!"# "5&--&Gy3S9JEM==,=:(&'3&-36789S—2Y3
&B3y3S9JEM=N13A'Z3.&:@E„:9;Q92,k66+6A" ?*[-'k64'
_A-4 <'Q3AP.2n9X@K3& p'Q3ANO3A@13A;&1E&[9>,;r&'-/3&7@13A;r
&'->P'(!36 <3/@13AD'E3A&[9>4>444
*) Tài liệu học tập chương 6
)47B3A'(e3G3&)ttt/5V"& / $/&,~'K+03 :1NO9/,C 4
$47B3A'(e3G3&$##)/W+5X"& ; $/&,~'K+03 :1NO9/,C 4
*) Câu hỏi, bài tập và đề tài thảo luận chương 6
Câu)4u3A&8.&E NE16C3A6 p'&1,9X.&7B3A>'P3AAX9>Y 3&E'4
Câu$4@7U3A&8.&E NE16C3A9X.&7B3A>'P3AAX93&73A9Xy3SAX9;&:93&E'4
CâuL4&M3W9&=CNE16C3A'y3&1,3&,3&u3A9:96C3A6 p'&1,4
Câua4 5'N ˜3NE16C3A+o3AS.&Q94

Câud4_CSQ3ANO3A9JES e'M=@13A;r&'-4
24
GE" 8"]

CHƯƠNG 7
Nhiệt động lực học
 !"#$%&'(!") !*+,  /&012'-3") !
*) Mục tiêu:
)4 5';&: 3 <=@I3A&: >r=P`> =P/9:9.&7B3A@G3&@I3A&: 9JE;&W2W7c3A4
$4 5'>,>-3NO3A67899:93A'(e32W9JE3& <6C3A2T9&[9/>-3NO3A9&1=CS>WNOW3&
n3@1.(>,A 0 +,  3& <6C3A2T9&[94
L4 5'9:9%3A&rE>,Q3ANO3A9JE9:93A'(e32W9JE3& <6C3A2T9&[94
7.1. Các phương trình trạng thái của khí lí tưởng
q4)4)4_CS;&: 3 <==c6y'
G@Z*&A+ &A
:9W3&9&K9JE=C>-+ 5'& <3@I3A&: 9JE>-6X>,E9X&5Nl3A=C &8.9:9
W3&9&K65j:96V3&@I3A&: 9JE=C>-4@I3A&: 9JE=C>-6789j:96V3&+c =C &8.
j:96V3&9:96I 2783A>-2%4:96I 2783A>-2%3,(6789A[ 2,9:9Z*&A4
@I3A&: 9JE=C>-6789j:96V3&+c 3& p'&P3AS@I3A&: 4&]3A&<&Q9A ]E
9:9&P3AS@I3A&: 9JE=C>-A[ 2,3&]3A &A9JE>-6X4
@I3A&: 9JE=C;& ;&W3&K6V3&/3A7U ENl3A+E&P3AS@I3A&: "&5W9&/
:.S'K.>,3& <6C9JE;& ;&W4 ]E+E&P3AS9X=C2 e3&<6789+ 5'N ˜3+c =C
.&7B3A@G3&@I3A&: >Y NI3Au3AD':3&7SE'"¡.//g# q`2
 <9;&01S:NI3A9O&59JE.&7B3A@G3&@I3A&: 2,=C@13A3&]3A>K36p9B+03
9JE3& <&[94E'6M(E&•(jk9&  !&E &P3AS":.S'K>,3& <6C4
GYA6A*<+"#
E…*<¢.S'K2,=C6I 2783A>-2%9XA :@V+o3A2T93k3>'P3AAX92e3=C6B3>VN <3
W9&"

†


∆
=
4@13A&<6B3>V:.S'K2,STm6

9;&E(A-Sp-9A1, @E6561:.S'K/
3A7U E9w3Nl3A9:96B3>V;&:9456u 9:96B3>VENl3A&<&Q9SE'")EgqLh==Ag
t/s)4)#
a
x=
$
4
29T"#& <6C2,6I 2783A>-2%6?9@73A9&1=Q96C9&'(536C3A&‰321I3.&M3ƒ
9JE9:9>-4[ 2,3& <6C@13A&E3A'(<6 /2,3& <6C@13A&E3A+:9&.&M3/E9X
9P3A&Q9"gz$qL/)h4@13A9:9W3&1:36B3A 03E&7U3A2K("gz$qL4
q4)4$4:96V3&2'-&T93A& <=>p9&K;&W
G/05WZ5t)-Z
P 2B)hht>,_E@ P)hqh3A& e39Q'D':@G3&6F3A
3& <9JE9:99&K;&W/6•G=@E6V3&2'-SE'6M("
@'A"],-6#MMX;!X†
50LA*<;-JAMAX*,-!X+
A*<,-MMX5+6#P*s'*
GIA"05H-tfN
‚=)s##/3A& e39Q'9:9D':@G3&6F3AW9&>,6F3A:.
9JE9:99&K;&WE(`''(jm96•G=@E3&]3A6V3&2'-SE'6M("
E@'A"]X,-6#MMX;A*<†5L"#"
xp @ '*=
25