physics i prof. zhiwei ma 马志为 浙江大学聚变理论与模拟中心 institute for fusion...
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Physics I
Prof. Zhiwei Ma
马志为浙江大学聚变理论与模拟中心
Institute for Fusion Theory and SimulationTel: 87953964(O)
Email: [email protected]
PPT download: http://ifts.zju.edu.cn/~zwma/ptwl_1
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Welcome to
There are several components:• Rehearse (reading assignments ) due before lecture
• Lectures (presentations, demonstrations)
• Homework (15% in total)
• Mid Exam (25% in total)
• Final Exam (60% in total)
• Labs (hands-on interactions with the phenomena)
• Do not miss lab;
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The Challenges of Physics I
1. The course is a few of NEW concepts!!- Many concepts have been learnt during a high school.- These old concepts are extended.
2. Math is the language of physics and here you need to learn to work with it- calculus: line integrals, surface integrals, gradients- vectors: addition, dot-product, cross-product, decomposition
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How to Succeed in Phys I…..1. Rehearse, and exercises before lecture
- I’ll keep them to a minimum
2. Don’t get behind!!3. Ask questions early if you don’t understand things
- in lecture ask me!! …also see me after class.- office hours in my office (Room 414-1, Bd No.11 in YuQuan) and maybe elsewhere.- make appointments outside of scheduled office hours.
4. Use problem solving to develop conceptual understanding- this is how you really learn science…
5. Your attitude, not your aptitude, will determine your altitude.5. Your attitude, not your aptitude, will determine your altitude.
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Where do the wind come ？Why the snow is white？
Curiosity to natural phenomena
Thinking, Questions, Trying to find answer
No thinking No question No progress!
•Mechanics•Thermodynamics•Electromagnetism
•Optics
PHYSICS
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•Mechanics•Thermodynamics
PHYSICS 1
environment force body motion
Force law
Motion law
One particleMany particles In random
averageEKv , ,
ondistrobuti( ), ( )f v f E
VpT , ,
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PHYSICSResnick, Halliday,
Krane23/4/18 zwma 11
Chap.1 Measurement
Experiment is the base of
PHYSICS
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Experiment is the base of
PHYSICS
Length, mass, time, force,Speed, density, temperature
Current, magnetic field strength
Physical Quantities
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Experiment is the base of
PHYSICS
Length, mass, time, force,Speed, density, temperature
Current, magnetic field strength
Physical Quantities
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Mass ( kilogram, Kg)
Standard of Mass as “Prototype Kilogram No. 20”
Standards and Units
Mass of 12C atom kgu 2710661.11
2627
16.02 10
1.661 10
kg
kg
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Galaxy 1043 kgsun 1030 kg
Earth 1024 kgperson 101 kg
virus 10-15 kg
atom 10-27 kg
electron 10-31 kg23/4/18 zwma 18
Time (second, s)
1 s = 9192631770 vibration of radiation emitted by
a cesium atom
Standards and Units
1year1
365 24 60 60s
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1-3 The Standard of TimeNIST-F1
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Length (meter, m)
Traveled by light in vacuum during a time of 1/299792456 second
Standards and Units
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10-3 10-4 10-5 10-6 10-7 10-8 10-9 10-10 m
Microscope
Electron Microscope
Size of atom
Scanning Tunneling Microscopes (STM)
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Scanning Tunneling Microscopes (STM)
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Si(111) Surface
mm 11
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Si(111) Surface
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Length
1 yard = 0.9144 meter1 inch = 2.54 centimeters
1 light•year = 9.48 x 1015m
Non-standards Units
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Mass
1 pound = 0.454 Kg1 ounce = 0.02835 Kg
Non-standards Units
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1-6 Precision and Significant figures
Rule 1: keep all digits up to the first doubtful one
Rule 2: the number of significant figures should not be enlarged in multiplying or dividing
Rule 3: In adding and subtracting, similar to rule 1
M, L and T
[x]=L
mass, Length and time
Dimension and dimensional analysis
[v]=LT-1
[a]=LT-2 [f]=MLT-2
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Circular motion
2[ ][ ]
[ ]c
va
r
Centripetal acceleration ac=v2/r
ac
Example
2LT 2( / )L T
L
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[ ]
dimensional exponents
Q L M T
、 、
p qv g h
1 1 2p q p
1 2 1 2v g h 2v gh
1LT 1 1
2 2
p q
Free fallExample
2
pqL
LT
( ) 2p q pL T
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20 0
1
2r r v t at
L
Constant acceleration motion
Example
LT
T
L 22
LT
T
L L L
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Chapter 2
Motion in 1-D
(Kinematics)23/4/18 zwma 35
Length, mass, time, force,Speed, density, temperature
Current, magnetic field strength
Physical Quantities
Vectors and Scalars Scalars magnitude Vectors both magnitude and direction
Length, mass, time, force,Speed, density, temperature
Current, magnetic field strengthSpeed of light in vacuum
83.00 10 /m sProton mass
271.67 10 kg
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Vector•To display a Vector
•Vector Calculation
•Vector Application
magnitude direction
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Magnitude
Properties of vectors
x
y
a
φ
xa
ya 22yx aaa
cosaax sinaay
Direction aa or
x
y
a
a1tan
jaiaa yxˆˆ
Unit vector1ˆˆ ji23/4/18 zwma 38
Three dimensionskajaiaa zyxˆˆˆ
222
zyxaaaa
a
axay
az
i
j
k
auaa ˆ Magnitude
unit vector
1 1ˆ aa uoru23/4/18 zwma 39
ADDING VECTORS
Making a Parallel Quadrilateral
B C
A+B = C
AB
Making a Triangle23/4/18 zwma 40
F=A+B+C+D+E
F
E
A
B
C
D
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A-B=C
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A-B=C A+(-B)=C
AB
B
-BC
CA=B+C
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kajaiaa zyxˆˆˆ
kbjbibb zyxˆˆˆ
bac
)ˆˆˆ(
)ˆˆˆ(
kbjbib
kajaia
zyx
zyx
kba
jba
iba
zz
yy
xx
ˆ)(
ˆ)(
ˆ)(
a
axay
az
i
j
k
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MULTIPLYING OF VECTORS
aB = C
A.B = c
AxB = C vector
vector
scalar
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kbjbibB zyxˆˆˆ
Direction no change
Magnitude change
aB = C
B
C
BaC
kabjabiab zyxˆˆˆ
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Multiplying of vectors
A.B = c
A
B
= A B cos
cosBAAB
BA
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A
B
C = A B sin
C
AxB = C ?AB
BABAAB
sin
AB
BAAB
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kikjji ˆˆ ˆˆ ˆˆ 0 0 0
i
j
k
kkjjii ˆˆ ˆˆ ˆˆ 1 1 1
kkjjii ˆˆˆˆˆˆ 0 0 0
kikjji ˆˆˆˆˆˆ jik ˆ ˆ ˆ
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Multiplying of vectors
bac
)ˆˆˆ()ˆˆˆ( kbjbibkajaia zyxzyx
zzyyxx bababa
kajaiaa zyxˆˆˆ
kbjbibb zyxˆˆˆ
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Multiplying of vectors
bac
)ˆˆˆ()ˆˆˆ( kbjbibkajaia zyxzyx
k ) b- a b(a
j ) b- a b (ai ) b- a b(a
xyyx
zxxzyzzy
ˆ
ˆˆ
kajaiaa zyxˆˆˆ
kbjbibb zyxˆˆˆ
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A+B = B+A
A.B = B.AAxB = - BxA
(sA)xB=Ax(sB)=s(AxB)
A. (B+C)= A.B+ A.CAx (B +C) =AxB+AxC
A .(BxC)=B .(CxA)=C .(AxB)
Ax(BxC)=(A . C)B-(A . B)C23/4/18 zwma 52
]ˆ)(ˆ)(ˆ)[()ˆˆˆ( 132131132332321 kcbcbjcbcbicbcbkajaia
kcbacbacbacba
jcbacbacbacba
icbacbacbacba
ˆ)(
ˆ)(
ˆ)(
232311322131
121233211323
313122133212
CBABCA$
))( (
)ˆˆˆ)](ˆˆˆ()ˆˆˆ[(
)ˆˆˆ)](ˆˆˆ()ˆˆˆ[(
321321321
321321321
kcjcickbjbibkajaia
kbjbibkcjcickajaia
)ˆˆˆ)((
)ˆˆˆ)((
321332211
321332211
kcjcicbababa
kbjbibcacaca
)]ˆˆˆ()ˆˆˆ[()ˆˆˆ( 321321321 kcjcickbjbibkajaia)CB(A
CBABCACBA
)()()(
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Derivation
( )( ) ( )( ) ˆˆ ˆyx zda tda t da tdA t
i j kdt dt dt dt
ktajtaitatA zyxˆ)(ˆ)(ˆ)()(
Integral
k(t)dtaj(t)dtai(t)dta(t)dtA zyxˆˆˆ
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plane polar coordinates
jaiaA yxˆˆ
i
ju
ruvectorsunittheareuandur ˆ ˆ
1 ˆ ˆ uur
jiurˆsinˆcosˆ
jiu ˆcosˆsinˆ
ruaA ˆ
jdt
dai
dt
da
dt
Ad yx ˆˆ
rudt
da
dt
Adˆ
dt
uda rˆ
j
dt
di
dt
d
dt
ud r ˆcosˆsinˆ
u
dt
dˆ
jdt
di
dt
d
dt
ud ˆsinˆcosˆ ru
dt
dˆ
u
dt
dau
dt
da
dt
Adr ˆˆ
ˆ ˆ( sin cos )
di j
dt
ˆ ˆ(cos sin ) d
i jdt
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plane polar coordinates
i
j
ruu
d
'u ru'ˆud ˆ dduud ˆ
dt
d
dt
ud ˆ
rudt
d
dt
udˆ
ˆ
udt
d
dt
ud r ˆˆ
jdt
di
dt
d
dt
ud r ˆcosˆsinˆ
u
dt
dˆ
jdt
di
dt
d
dt
ud ˆsinˆcosˆ ru
dt
dˆ
ˆ ˆ( sin cos ) d
i jdt
ˆ ˆ(cos sin ) d
i jdt
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Vector•To display a Vector
•Vector Calculation
•Vector Application
magnitude direction
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W = F . s cos
Example
F
W = F . s
sHow to calculate the work?
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Example
How to display the rotation?
rv
r
v
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N
S
W E
(1,1)
(-1,2)
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N
S
W E
(1,1)1r2r
position vectors1r
2r
r
Difference of 1r
2r
rrr 12
r
is vector too
(-1,2)
Displacement
ˆ ˆi j ˆ ˆ2i j
ˆ ˆ2i j
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Position, velocity and Acceleration
r
x
y
z positionr is function of time t: r=r(t). ktzjtyitxtr ˆ)(ˆ)(ˆ)()(
ktzjtyitxtr ˆ)'(ˆ)'(ˆ)'()'('
'r
r
)()(' trtrr
Displacement
kzjyix ˆˆˆ
vt
r
Average Velocity
vt
r
t
lim
0
kdt
dzj
dt
dyi
dt
dx
dt
rd ˆˆˆ 0t
Instantaneous Velocity
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Position, velocity and Acceleration
ktvjtvitvtv zyxˆ)(ˆ)(ˆ)()(
)()(' tvtvv r
x
y
z position
'r
r
Displacement
kvjviv zyxˆˆˆ
at
v
Average acceleration
at
v
t
lim
0
Instantaneous acceleration
kdt
dvj
dt
dvi
dt
dv
dt
vd zyx ˆˆˆ
ktvjtvitvtv zyxˆ)'(ˆ)'(ˆ)'()'('
0tk
dt
zdj
dt
ydi
dt
xd
dt
rd ˆˆˆ2
2
2
2
2
2
2
2
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x(t)0x=x(t)
Motion in one dimension
dt
tdxtv
)()(
dt
tdvta
)()(
2
2 )(
dt
txd
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t
X(t)
0
AX=A
X=A+BtX=A+Bt+Ct2
X=Dsin(t+)
0dt
dxv
0dt
dva
0
dt
dva
Bdt
dxvC
dt
dva
CtBdt
dxv
2
2
)cos( tDdt
dxv)sin(2 tD
dt
dva
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x(t)
tt0
Slope at t0
Slope at t0
v(t)
tt0
0
0tt
tt dt
dxv
0
0
tttt dt
dva
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Motion with constant acceleration
Slope
x(t)
t
v(t)
t
Slope
a(t)
t
Slope=0
x=A+Bt+Ct2 CtBdt
dxv 2 C
dt
dva 2
0dt
da
B
2C
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Motion with constant acceleration
dt
vda
dt
rdv
dtavd
v
v
t
tdtavd
0 0
)( 00 ttavv )0( 00 tatvv
dtvrd
r
r
tdtvrd
0 0
200 2
1attvrr
r
r
tdtatvrd
0 0 0 )(
220 0)(2 vvrra
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Freely Falling Bodies
ga y
0
g
289 m/s.g
gdt
dv gtv
dt
dyv
t
gtdt0
gdtdv
vdtdy ty
vdtyd00
v t
gdtdv0 0
2
2
1gt
2
2
1gty
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ExercisesP46-48 7, 9, 11, 12, 24, 32, 34P78-81 11, 19, 24, 30, 46, 50
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