南京大学大学物理肖明文班作业01

bi a j 2 ij
0 i j ij 1 i j
Problem 1.19(optional)
m v qv B qB v
We may set
q B v m While B is known, v is arbitrary. So q q B B lv m m
Problem 1.1
(a)1ps =10–12s 1fs = 10–15s (b) 1nm =10–9m; (c) 1MeV =106eV 1GeV =109eV
Problem 1.3 The mass of the earth
m 10mol 6.022 10 6.022 10 kg
Cosine of the angle included is
cos S B R 2 sin(124) sin(48)[cos(151) cos( 71) sin(151) sin( 71)] cos(124) cos(48) 0.832
arccos( 0.832) 146 2.55 80
Scheme 1
me 2 G me c r Gme r 2 c
Gravitational radius (4.2.13):
2
2Gm r 2 c
Scheme 2 Find a wavelength l ~ r
A wavelength may corresponds to an energy
S ( R, 90 34 124, 151); B ( R, 90 42 48, 71 or 289)
Displacement vector is S – B. Convert into Cartesian system
er cosq k sinq cosj i sinj j
Set and we have
1 e 4 0 r
2
1 e 2 me c 4 0 r
2
2
1 e 15 r 2 . 82 10 m 2 4 0 me c
(see section 15.5)
Incorporating some universal constant(s) in we might get some results for a length related: G, h, etc.

Problem 1.5
1 15 26 lg x lg 10 lg 10 5.5; 2 5.5 5 x 10 3.16 10 ; 1 15 26 ln x ln 10 ln 10 2

logarithmic scale



5.5 ln 10 same
Problem 1.8
h
hc
It may correlate to energy of a microscopic particle. Set hc
l
We have Compton wavelength Eq.(22.3.3):
l
me c
2
h l me c
Other possibilities
a0 4 0 2 mee
1 R
2

2 3 3 64 0 c 4 mee
……
Problem 1.12 Solution: At extreme low temperature,
CV = g T
Problem 1.14
A ( B C ) B( A C ) C ( A B)
polar vector
24
24百度文库
23
mol 1kg
24
6.022 10 5.98 10 accuracy 24 5.98 10 0.702%
Problem 1.4 the number of seconds in a year
10 365.24 86400 0.446% 365.24 86400
Problem 1.17
a3 a1 a 2 a3 b2 2 , b1 2 a1 a 2 a3 a1 a 2 a3 a1 a2 b3 2 a1 a2 a3
(triple products in denominators are cyclic)
See Eq.(9.5.5) for details
Problem 1.21
Greenwich as x-axis, longitude is j, (north or south) latitude is l = 90º – q ; or q – 90º
In spherical system the position vectors are
“Straight line” distance is arc!
arc 6.370 10 km 2.55 1.62 10 km
3
4
Gm R
One way:

12
G m R

Alternatively: similar to v2 = 2as
m v ~ gR ~ G 2 R R
2
Problem 1.9 (optional) Similar to gravitational self-energy, electrostatic self-energy is