0
1.a)proof, ds/dt = u+at and integrate
b)4.19*10^-10 J
2.a) i) 6.75*10^-3 kg m^2
ii)A)proof, 45rpm = 90pi rev/min = 4.7rad/s
ii)B)3.1rad/s^2
iii)3.6rad/s
iv)further from axis of rotation, increased central force required, friction can't provide this so it slides off
b)angular velocity increases as moment of inertia decreases and angular momentum is conserved
3.a)i)1.98*10^20 N
ii)1020m/s
iii)work done in bringing 1kg mass from infinity to that point
iv)7.6*10^28 J
v)-3.8*10^28 J
b)i)proof, equate kinetic energy and potential energy
ii)2400m/s
4.a)force acting on object is proportional to and in opposite direction to displacement
b)Wasn't entirely sure what they were looking for here. Presumably both y=0.05cos(200pi t) and y=0.05sin(200pi t) are acceptable.
c)1.9*10^4 m/s^2
d)9.5*10^3 N
e)240J
5.a)i)proof
ii)potential at B 92V, so pd 138V
b)bring charged rod close, touch sphere with finger to repel electrons to earth, remove finger then remove charged rod leaving positively charged sphere
c)i)electrostatic force up, weight down
ii)1.92*10^-18 C
iii)12
d)Millikan conjectured that electronic charge is the fundamental charge unit and all charges can be expressed as integer multiples of this. Down quark has charge of e/3 so that's a contradiction.
6.a)Proof. Use v(perp) = v sin69
b)i)2.1*10^-4N
ii)East (I think)
c)Zero, parallel to magnetic field
d)i)0.012m
ii)Cylinder around the wire? Not sure what they were looking for here (I think I got this wrong in the exam, see earlier in thread).
7.a)i)Change in current --> changing magnetic field --> emf across inductor which opposes buildup of current --> time delay in max brightness being reached
ii)0.25A
iii)2.4H
iv)A)presumably resistance stays the same so max current is unchanged
B)takes longer
b)switch off current, changing magnetic field induces large emf for short period of time over inductor hence large pd for short period of time over neon lamp
8.a)i)A)4.75*10^7 m/s
B)8.23*10^7 m/s
ii)perpendicular compenent accelerated into uniform circular motion, parallel component unchanged, recombine and helical motion obtained
b)i)proof, equate central force and magnetic force
ii)1.6*10^-10 s
iii) 7.6*10^-3m
c)circles off in opposite direction, larger radius for circular motion (or greater pitch for helix I think)
9.a)y=0.05sin2pi(3t - x/0.02)
b)y=0.05sin2pi(3t + x/0.02)
c)0.035m
10.a)i)A)pi rad
B)pi rad
ii)optical path difference between the two reflected rays. if optical path difference = (m+0.5)lambda then for this lambda we have destructive interference hence wavelength lambda blocked.
iii)wouldn't get a very pretty picture otherwise
iv)580nm
b)measure space between succesive fringes (with travelling microscope) and measure length of glass plates. Find wavelength of sodium light. Use d=(lambda l)(2 deltax)
11.a)proof. nodes are lambda/2 apart, find lambda
b)(75+/-4)m/s
c)i)Although percentage uncertainty is overall decreased, increasing frequency increases speed of wave and this actually means that the absolute error is larger. Not totally sure about this one though, maybe the wavelength decreases instead.
ii)Measure space between several nodes and scale down.
There's likely to be a few things wrong in there, particularly explanations
