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...
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...
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...
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...
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...
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...
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...
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...
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...
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 ##...
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...
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?
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...
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...
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##...
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...
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...
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...
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...
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} ##...
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...
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...
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...
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?
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...