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Physics Exam Answers: Autumn Semester 2004-5
Level One
F31AB1: Biophysics
1)
Spots 249 nm. apart can be distinguished.
2)
Pressure amplitude = 2.9  10-4 Nm-2 ; Velocity amplitude = 6.7  10-7 ms-1.
6)
(c) Action potential is triggered. (d) t = 0.45 μs. (e) Na+ (out) = 560.8 mM;
C = 0.89 μF cm-1.
7)
(b) Time = 0.5 s.
8)
Velocity = 20.5 ms-1 ; Resonant freq = 21 MHz.
(c) 262 k bytes.
F31AM1: Mechanics I
1)
Minimum time (South) = 120 s. ; Shortest time (West) = 89.4 s.
2)
TA = 59.52 N; TAB = 44.64 N; TBC = 19.84 N.
3)
(a) I = ma2/12; (b) I = m(a2 + b2)/12; (c) I = m(a2 + b2)/3.
4)
Work (OAB) = kl2m3; Work (OCB) = klm2; Force not conservative.
5)
Angular speed = 1.1 rad s-1.
6)
Speed = 9113.9 ms-1.
7)
vobs = 4.47 ms-1 ; aobs = 3.88 ms-2.
8)
(b) Centrifugal force is 1663.5 N directed outward from local centre;
Coriolis force is 1454 N directed outward from local centre.
F31ARM/ F31YMC: Modelling
1)
df/f = 1/60; Frequency unchanged by volume change.
2)
(a) BC (T=0) = B0 ; (b)  = 2B0/TC valid for t<<TC.
2
3)
Dimensions: ρ [ML-3];  [MT-2].
4)
(a) Mass of disc = a2t(p + 2/3 qa); (b) Mass of sphere = a4s.
(c) R 
5)
 r
.
2bl
(a) u (t ) 
kt
u0 k   m 
m

g

g

e



 ; (b) Force = mg – u0k.
k 
m 


F31AV1: Environmental Physics I
1)
t = 8.6  109 years.
2)
Power = 36.5 kW .
3)
Max Power = 1.147 kW ; TH = 171˚C
6)Annual power available = 66.5 MW.
7) TE = 285 K ; eT = 0.96
F31AZ1: Introduction to Electromagnetism
1)
E = 5.12  1011 Vm-1 ; Force = 8.20  10-8 N towards proton.
2)
i = - 4.3 A ;  = 5.7  10-16 s.
3)
Esurface = 1.8  105 Vm-1 ; Einside = 0
4)
Equivalent R = 17.5  ; Current = 0.8 A
5)
C = 7  10-4 Farad ; Qmax = 1.37  1010 C
6)
Smallest magnetic field = 0.275 T
7)
(b) C = 4.23  10-10 F. (c) I = 0.020 A. (d) I = 0.27  10-3 A.
8)
(a) I7V = 4/7 A. ; I8V = 11/7 A. ; Power = 13.7 W. (b) B = 3  10-3 T.
3
Level Two
F32AA4: The Structure of Stars
2)
(a) Teff  4100 K.
4)
6)
7)
(a) Mstar  2.7 Solar Masses
(c) E = -4.07  1041 J.
(c) RS = 3.3  107 m. or 0.047 Solar radii.
F32AB2: Biomedical Physics II
1)
2)
3)
5)
6)
7)
8)
Valve opens at t 0.15 s. and closes at t  0.45 s.
Residual volume = 0.75 l.
CMoutput = 0.3 V.
Cardiac output = 74 ml s-1.
VIII = -0.2 mV ;   7˚; Pulse duration is 4ms and energy deposited is 173 J.
Source image distance = 75 cm ; Image size = 0.882 mm.
(a) Anterior dose per fraction = 0.8 Gy; Oblique dose per fraction =1.2 Gy for both
fields; (b) Max skin dose = 0.24 Gy per fraction.
F32AM4: Elements of Mathematical Physics
1)

 2ax
F = 
 ax 2  by 2  c 2



2
2
2
2 2 
ax  by  c 
 2a
 2b
which at (1,1) gives
,
2 2
(a  b  c )
( a  b  c 2 )2
4)
A0 = An = 0 ; Bn = -2(-1)n/n0 .
5)
cn =
6)
u(x,y) = (A cos x + B sin x) e
7)
.A = 3z2 ; Surface integral = 8 .
8)
G() =


,
 2by


1 eT  1
.
T   in 0
2
y
; u(x,y) =
1 2  2 cos 
.
2
2
4
2
3
sin 2x e 4 y
l
F32AQ1: Quantum Physics I
k 2
 .
m
1)
J
3)
Eigenvalue =1.
4)
x̂  0 ;
p̂x = 0 .
5)
P(E2) = sin2  ; after measurement wave fn. is 2 .
6)
(a) x  5.8 m. (b) y = 0 . Ground state energy = 0.44 meV;
K = 1/30 ; <E> = (E1 + 4E2 + 25E3)/30 .
8)
E0 =
3C 2
4m 2 2
F32AZ2:Electromagnetism 1
1)
E = 172 Vm-1 along square diagonal.
2)
E = -2A(x + 3y)i - 2A(x + 3y)j -6z2k ;  = -0 (20A + 12z)
3)
B = 3.1  10-4 T.
4)
Epeak = 2.5  104 Vm-1 ; Bpeak = 1.3  10-4 T.
5)
Total induced charge = -q .
7)
p = 40E0R3 ; max = 30E0 .
8)
Bspace = 0nI ; Hspace = nI ; Mspace = 0; Brod = 0RnI ; Hrod = nI ; Mrod = (R – 1) nI ;
5
Level 3
F33AA6: Cosmology
1)
h(t0) = 3ct0 .
2)
N  400 cm-3 .
7)
(b) Min. redshift Z  2.5  109 .
F33AB5: Medical Imaging
3)
pH = 4.77
7)
R1 = 4.5 s-1 mM-1 ; T1 = 0.713 s. ; TE = T2* ; Signal change = 13.31 % .
8)
Number of evoked responses needed  450 .
F3CAM8: From Hamiltonians to Chaos
1)
y = (py – eBz)/me .
2)
D = (ln 2)/(ln (5/2)) .
4)
Choose r = (n/m)2 where n and m are integers.
5)
sin  2 g
  sin  0
Eqn. of motion for bead: (1  cos ) 
2
2a
6)
Lyapunov exponent () = ln 2 ; Mapping chaotic when  > ½ .
8)
(a) L =
m 2 2
g
l   mgl cos ; (b)   sin  0 .
2
l
(2  2 ) g
(2  2 ) g
Normal modes are : 1 
; 2 
.
l
l
F33AN3: Nuclear Physics
1)
 = 2.76 b. ; phase shift = 13.3º .
2)
Mass = 658 MeV.
3)
Age = 6529 Years.
4)
Violates parity conservation.
6
5)
Orbital electron capture.
6)
 = 4 (A + B/3) ; (a) total fraction scattered = 6.3  10-9 ; (b) fraction to detector =
7)
Compound nucleus is Li37 ; v () = 3.3  10-2 c ;
6  10-15 ; count rate = 1.875 Hz .
v (H13) = 4.4  10-2 c .
F33AS1: Solid State I
1)
Cohesive energy = -4.07 eV.
3)
Packing fraction = 0.34 .
5)
kF = (2n)½ where n is electron density; for polarised gas, kF increase factor is 2.
6)
R0 = 2.99  10-10 m. ; cohesive energy per atom = -0.0267 eV.
7)
Emin (X-rays) = 2639 eV; Emin (Electrons) = 4.53 eV ; F (Gold) = 5.50 eV.
8)
me* = 0.42 me ; mh* = 0.85 me .
F33AT3: Quantum Statistics
2)
RMS (Xe) = 239 ms-1 .
3)
Prob. of 6 particles on site = 0.0076
4)
n( k )dk 
5)
TC = 1.5 microkelvin.
6)
Debye freq. D = s
8)
TF = 2.64  10-2 K ; CV = 1.55 JK-1 .
 2 N  ( k ) / k B T
ke
dk
mkBT
8 N
.
A
F33AZ3: Electromagnetism II
3)
N  57 atoms.
5)
B = 56.3º ; E field compt. of reflected beam is perpendicular to plane of incidence.
7
6)
G.B = 1368 T2 m-1 , so a solenoid of B = 13 T requires a gradient of  100 Tm-1.
7)
Quarter wave coatings: air  cryolite  aluminium oxide  glass.
8