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  1. bananabandana

    Confused about voltage & current -- Please check my understanding

    Seems about right! :) I don't know what you're wanting to do (are you an engineer, is this a hobby, etc.?) but another good resource is the Feynman lectures Vol II - http://www.feynmanlectures.caltech.edu/II_01.html You can't really dip in and out of them - it's probably best to make time to...
  2. bananabandana

    Angular momentum of a rotating door

    Ah, of course. No, it's definitely not rotating about S. Thank you. Also realise now that the definition of the intertia tensor only involves motion about the centre of mass, so obviously it doesn't take the angular momentum relative to the origin at $S$ into account. So then I get this- that...
  3. bananabandana

    Angular momentum of a rotating door

    Why aren't the two the same? Surely the whole system is connected and therefore has the same ##\omega##
  4. bananabandana

    Angular momentum of a rotating door

    Ah no, sorry - it should be ##L## . This was part of a final year exam question, so I'm pretty sure I must be wrong somewhere!
  5. bananabandana

    Angular momentum of a rotating door

    Homework Statement A door ( a rod of length ##L##, mass ##M##) rotates with angular velocity ##\omega## about a point ## H ##, and approaches a stop at ##S##. ##H## and ##S## are along the same line, and separated by a distance ## s ##. Show that the angular momentum of the door about the point...
  6. bananabandana

    Rayleigh Criterion Question

    Homework Statement 'A scientist wants to take a picture of a distant yellow object using a pinhole camera such that the picture is of maximum sharpness. Let ##\lambda## =wavelength of yellow light, ##d## = diameter of pinhole, ##D = ## distance of pinhole to film. Find ##d##. Homework...
  7. bananabandana

    Torque question (qualitative)

    I'm not sure what level of explanation you want... Most simply, torque is a turning moment. The idea of torque is that if you apply a force at a greater distance, you get a bigger rotation - it would be easier to swing a cat by its tail than its middle (if you wished to swing cats), and it...
  8. bananabandana

    Plane Wave at Barrier

    Homework Statement Sorry for the dull question. Problem is as shown/attached Homework Equations The waves in part ii) are travelling in a HIL dielectric of permittivity ##\epsilon_{r}## from ##0 <z<d## and then hit an ideal metal boundary at ##z=d##. The Attempt at a Solution I figure this...
  9. bananabandana

    Stirring a Cup of Tea

    The change in entropy of the surroundings is zero? Like I said above? Or, from equation (1) since the surroundings are a heat bath, there is no change in temperature, therefore no change in entropy...? Phase rule makes sense, had to look it up -## F= C-P+2## - in this case, ## C=1## (assuming...
  10. bananabandana

    Stirring a Cup of Tea

    That's what they put in the question! I'm assuming that the work went out as heat into the surroundings when the tea cooled?
  11. bananabandana

    Stirring a Cup of Tea

    Also - regarding the point about entropy and state variables. Is there an intuitive justification of the fact that any given state variable ##S,U##etc., can be written explicitly in terms of only two variables i.e ## S=S(T,P)=S(V,N)## or do I need to start doing some more theoretical...
  12. bananabandana

    Stirring a Cup of Tea

    Ah, I see. I'm guessing you're wanting me to say the ##dS=0## - since the temperature of the tea at the end will be the same as the temperature at the beginning. I guess that makes sense for the tea - like I said earlier, it seems sensible that the tea loses all the extra internal energy it...
  13. bananabandana

    Stirring a Cup of Tea

    Yes, volume is ##2.5 \times 10^{-4}m^{3}## - I've found the general expression for the change in the entropy of the universe and the tea in eqns (1) and (2),above? [These were the results given to derive, so I assume they're right!] To get a numerical answer, I would just stick in ##...
  14. bananabandana

    Stirring a Cup of Tea

    Homework Statement A mug containing a volume of ta initially at 90oC is in thermal contact with the enivronment at 20oC. Density of tea = ##10^{3}kgm^{-3}## Constant pressure specific heat capacity of tea: ##4.20 \times 10^{3} Jkg^{-1}K^{-1}## ... b) After reaching equilibrium, 0.01 J of...
  15. bananabandana

    Double Paralell Plate Capacitor with Dielectric

    I think there should definitely be a factor of 1/2 - this is because the charge density is split between the top and bottom plates. -Gauss's law for a flat sheet?
  16. bananabandana

    Double Paralell Plate Capacitor with Dielectric

    Ah yes, that was very stupid - I should be adding the capacitance. The equation for the voltage is also wrong: it should read: $$ V=\frac{3Qd}{2\epsilon_{0}A(1+\epsilon_{r})} $$. I made a typo. This means I now have a result: $$C = \frac{\epsilon_{0}A(1+\epsilon_{r})}{3d}$$ So I'm out by a...
  17. bananabandana

    Double Paralell Plate Capacitor with Dielectric

    Homework Statement Please see attached. Homework Equations The Attempt at a Solution I get a result of ## \alpha =\frac{1}{2} ## for part a) - which I think is correct. I'm stuck however on part b) - with the dielectrics. I have that the field in the region where the dielectric is...
  18. bananabandana

    Atwood Machine in Elevator

    Homework Statement Please see attached for diagram. We know that the elevator arm is horizontal when the lift is stationary, with ## M_{1}=\frac{4M_{2}M_{3}}{(M_{2}+M_{3})}## It wants us to find out if this is still the case when the lift is accelerated upwards at a constant velocity ##g##...
  19. bananabandana

    Longitudinal Wave Equation from Transverse One

    Homework Statement Please see attached. Part ii) Homework Equations The Attempt at a Solution So I try to conserve volume as it suggests in the hint. I take the initial volume of the region to be given by: $$ h \times \delta x \times l = (\delta x + \eta) (h+\Psi) l $$ Where l is just some...
  20. bananabandana

    Bandwidth Theorem

    Okay, so long as that's all that it is, that's fine. I understand what you mean by the deltas and also find it really annoying to have all of them flying around with none of them being very precisely defined! To be honest, it's quite odd that it's in the course at all given no Fourier - i.e it...
  21. bananabandana

    Bandwidth Theorem

    Firstly, thanks for all the work, and very sorry for the slow reply on my part. Yes, this is a direct quote from my course notes. It's very strange. This source suggests that the answer is ##\sigma_{t}\sigma_{f} = \frac{1}{4\pi} ##. As does this one, from University of Toronto. They are using a...
  22. bananabandana

    Bandwidth Theorem

    Homework Statement Consider a propagating wavepacket with initial length ## L_{0}##. Use the bandwidth theorem to show that the minimum range of angular frequencies present in the wavepacket is approximately: $$ \Delta{\omega}\approx \frac{v_{g}}{L_{0}} $$ Homework Equations Bandwidth theorem...
  23. bananabandana

    Energy of a Forced, Damped Oscilator

    Oh, oops .The expression for the potential energy is rubbish. Sorry. It should be: $$ E_{U} = \frac{1}{2}kA^{2}sin^{2}\omega t =\frac{1}{2}m\omega_{0}^{2}A^{2}sin^{2}\omega t $$ After that, I went through it again: I get that the kinetic energy plus the potential energy: ## E_{K}+E_{U} ##...
  24. bananabandana

    Frequency difference to find a 20m whale

    Homework Statement Please see attachment for diagram. The two boats are coherent sources of sound waves (phase difference ## \phi##) - i.e it's a double slit problem. Prove the formula given for ## y_{max}##. Suppose the whale is 20m long. How large should the sonar frequency ##f## be so that...
  25. bananabandana

    Energy of a Forced, Damped Oscilator

    Ah, I think I understand better now - can we say that if it's in a steady state that the loss of energy due to friction is equal to the energy which is input into the system by the driver? In that case, we just get back to the total energy being ## \frac{1}{2}m\omega^{2}A^{2} ##. ? By the way...
  26. bananabandana

    Energy of a Forced, Damped Oscilator

    PLEASE IGNORE ABOVE - OLDER VERSION WAS COPIED IN BY MISTAKE! APOLOGIES.
  27. bananabandana

    Energy of a Forced, Damped Oscilator

    Homework Statement A forced damped oscilator of mass ##m## has a displacement varying with time of ##x=Asin(\omega t) ## The restive force is ## -bv##. For a driving frequency ##\omega## that is less than the natural frequency ## \omega_{0}##, sketch graphs of potential energy, kinetic energy...
  28. bananabandana

    Energy in a Stationary Wave

    Yes, but a stationary wave is by definition formed from two travelling waves moving in opposite directions which means it can then be rewritten in the form that you suggest with the time and space separated? Or is that not right?
  29. bananabandana

    Energy in a Stationary Wave

    Homework Statement Show that the potential and kinetic energy densities for a stationary wave are not equal. Homework Equations A) The 1-D Wave Equation: $$ \frac{\partial^{2} \psi}{\partial x^{2}} = \frac{1}{v^{2}} \frac{\partial^{2}\psi}{\partial t^{2}}$$ B) The general form of a stationary...
  30. bananabandana

    Why, IF electrons really orbited atoms, would they lose energy?

    Oh right, for sure. The electron is at a different distance from the point! Sorry!
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