12. Motion in circle
- \(\omega = \frac{2\pi}{T}\)
- \(v_c = \omega r\)
- \(a_c = \omega^2 r\)
- \(F_c = ma_c = m\omega^2 r =
\frac{mv^2}{r}\)
13. Gravitational
fields
- \(F_g=\frac{Gm_1m_2}{r^2}\)
- For satellites: \(F_c = F_g\)
- \(g=\frac{GM}{r^2}\)
- \(\phi = -\frac{GM}{r}\)
- \(E_p = -\frac{GmM}{r}\)
Example Problems from Chapter
13
State Newton's law of
gravitation:
(把 \(F_g=\frac{Gm_1m_2}{r^2}\)
解释一遍)
| # |
Ans |
Mark |
| 1 |
Gravitational force is directly proportional to
product of masses |
(B1) |
| 2 |
... inversely proportional to the square of
their separation |
(B1) |
Why
is Gravitational Potential Energy (GPE) always negative?
| # |
Ans |
Mark |
| 1 |
Potential energy is zero at infinity |
(B1) |
| 2 |
Gravitational forces are attractive |
(B1) |
| 3 |
Work must be done on the object to move it to
infinity |
(B1) |
Total energy of a
satellite in orbit:
| # |
Ans |
Mark |
| 1 |
\(F_c=F_g, \left( \frac{GmM}{r^2} =
\frac{mv^2}{r} \right)\) |
(B1) |
| 2 |
\(E_k = \left( \frac{1}{2}mv^2 = \right)
\frac{GmM}{2r}\) |
(B1) |
| 3 |
\(E_p = \phi m =
-\frac{GmM}{r}\) |
(B1) |
| 4 |
\(E_t = E_k + E_p = \left( \frac{GmM}{2r}
- \frac{GmM}{r} = \right) -\frac{GmM}{2r}\) |
(B1) |
14. Temperature
- \(Q = cm\Delta t\)
- Absolute zero: \(0K
\approx -273.15^\circ C\)
15. Ideal Gases
- \(PV \varpropto T\) where \(T\) is the thermodynamic temperature
- \(PV = nRT = Nk_BT\)
- \(PV = \frac{1}{3} Nm\langle c^2 \rangle =
\frac{3}{2}Nk_BT\)
15章例题
What's meant by ideal
gas:
| # |
Ans |
Mark |
| 1 |
Gas that obey \(pV\varpropto
T\) OR \(pV=nkT=NRT\) |
(M1) |
| 2 |
Explain symbols;Pressure\(\times\)Volume=constant\(\times\)T |
(C1) |
\(N_A\) , Avogadro constant
| # |
Ans |
Mark |
| 1 |
Numbers of atoms |
(M1) |
| 2 |
...in 12g of Carbon \(C_{12}\) |
(A1) |
16. Thermodynamics
- \(\Delta U = Q + W\)
- \(\Delta U \varpropto T\)
- \(W = P\Delta V\)
16章例题
Reference
to molecular kinetic and potential energy,describeand explain the change
of interal energy
- Gas heated at constant volume, temperture increases
| # |
Ans |
Mark |
| 1 |
No change in separation so no change in PE |
(B1) |
| 2 |
Temperture increases so KE increases |
(B1) |
| 3 |
Total internal energy increases |
(B1) |
- Wire stretched within elastic limit at constant temperture
| # |
Ans |
Mark |
| 1 |
No change in temperture so no change in KE |
(B1) |
| 2 |
Stretch increase separation so increase in PE |
(B1) |
| 3 |
Total internal energy increases |
(B1) |
| # |
KE |
PE |
| Mechanical |
\(\frac{1}{2}mv^2\),\(v\)相对质心速度 |
\(\frac{1}{2}kx^2\),宏观胡克定律 |
| Internal |
\(KE_m\),分子热运动 |
\(PE_m\),intermolecular force,\(\frac{1}{2}kx^2\) |
Explain,
by reference to work done and heating, whether the internal energy of
the following
- Gas in ballon bursts suddenly
| # |
Ans |
Mark |
| 1 |
no thermal energy change |
(B1) |
| 2 |
Volume increase when burst(workdone against atmopshere) |
(M1) |
| 3 |
internal energy decreases |
(A1) |
- Ice melting at constant temperture & atmospheric pressure to
from water that denser than ice
| # |
Ans |
Mark |
| 1 |
Volume decreases when melting |
(B1) |
| 2 |
Heating the ice breaks the bond |
(M1) |
| 3 |
internal energy increases |
(A1) |
17. Oscillations
18. Electric Fields
电场强度 \(E =
\frac{F_e}{q}\)
匀电场
\(E = \frac{F_e}{q} =
\frac{V}{d}\)
电场力 \(F_e = E\times q =
\frac{V\times q}{d}\)
\(EPE = E_p = F\times d = V\times
q\)
库仑定律Coulomb's Law:
- \(F_e = \frac{k\times
qQ}{r^2}\text{, where } k = \frac{1}{4\pi \varepsilon
_0}\)
不均匀电场:
\(F_e = \frac{k\times qQ}{r^2}\text{,
where } k = \frac{1}{4\pi \varepsilon _0}\)
\(E = \frac{F_e}{q} = \frac{k\times
Q}{r^2}\)
\(EPE = \int^a_b F dr = \frac{k\times
qQ}{r}\)
\(E = \frac{F_e}{q} = \frac{k \cdot
Q}{r^2}\)
\(EPE = \int _b^a F dr = \frac{k \cdot
qQ}{r}\)
18章例题
State Coulomb's Law
| # |
Ans |
Mark |
| 1 |
Force proportional to product of charges
and inversely proportional to the square of the
separation |
(B1) |
| 2 |
...between two point charges |
(B1) |
19. Capacitance
20. Magnetic Fields
- Ampère's Force: \(F=BI\sin(\theta)\)
- 1
Example Problems from Chapter
20
State
what is menat by \(quantisation\) of
charge?
| # |
Ans |
Mark |
| 1 |
Charge exists in discrete and euqal
quantities |
(B1)any 1 |
| 1 |
Charge are all multiples of elementary
charge/e/\(1.6\times
10^{-19}C\) |
(B1) |
Define the Tesla
(Unit of \(B\))
把 \(F=BIsin(\theta)\)
的垂直情况变形成 \(B=\frac{F}{I}\)
然后解释
| # |
Ans |
Mark |
| 1 |
Uniform magnetic flux normal to a straight wire
carrying 1A current |
(M1) |
| 2 |
Creates a force per unit length |
(A1) |
给弹簧通电为什么会间距缩短?
| # |
Ans |
Mark |
| 1 |
Magnetic field in one loop (same current direction) |
(B1) |
| 2 |
Cuts and is normal to the second loop |
(B1) |
| 3 |
Causes an attractive force in the second loop |
(B1) |
| 4 |
Attractive force due to Newton's third law |
(B1) |
给平行导线通同方向随\(\sin t\)电流, 受力的变化
| # |
Ans |
Mark |
| 1 |
Force is always attractive (since current is in the
same direction) |
(B1) |
| 2 |
Varies from zero to maximum |
(B1) |
| 3 |
Force varies with twice the frequency of
current |
(B2, any 2) |
| 4 |
(OR) Force varies with \(\sin^2
t\) |
One per each |
带电粒子通过垂直匀磁场旋转半径关系式
- \(F_m=F_c\)
- \(Bvq=\frac{mv^2}{r}\)
- \(r=\frac{mv}{Bq}\), \(m,q\)一般在常数表
Hall \(V_H=\frac{BI}{ntq}\)
电场力磁场力受力平衡
右手螺旋定则画图……
21. Alternating
Currents
22. Quantum Physics
- Funciotns
- \(\lambda = \frac{h}{p}, p =
mv\)
- Kinetic energy: \(E_{photon} = hf
= \frac{hc}{\lambda}\)
- Momenton: \(p_{photon} =
\frac{E}{c} = \frac{h}{\lambda}\)
- Election proprties:
- Photoelectric effect: Shows
particle-like property of light.
- Electron diffraction: Shows
wave-like property of electrons.
- Photon:
- A packet of elecmatric radiation.
Example Problems from Chapter
22
Describe
the apperence of emission spectrum, as seen using a diffraction
gating
| # |
Ans |
Mark |
| 1 |
(Mostly)Dark backgournd |
(B1) |
| 2 |
coloured lines |
(B1) |
Describe the
photonelecrtric effect
| # |
Ans |
Mark |
| 1 |
Elecrtomagnetic radiditon incident on (metal)
surface |
(B1) |
| 2 |
Emission of electron |
(B1) |
23. Nuclear Physics
24. Medical Physics
25. Astronomy and
Cosmology
- Luminosity: \(L = \sigma
A T^4 = 4\pi \sigma r^2 T^4\)
Where \(A\) is the surface area of the
star.
- Radiant Flux Intensity: \(F = \frac{L}{A} = \frac{L}{4\pi
d^2}\)
Where \(A\) is the surface area of the
sphere with radius \(d\).
- \(F \varpropto \frac{1}{d^2}\)
- \(\frac{\Delta f}{f} = \frac{\Delta
\lambda}{\lambda} = \frac{v}{c}\)
- \(\lambda_{max}T = \text{constant} \
b(=0.0029mK)\)
- \(v = H_0 d\)
