@gneill Thanks so much for the clear answer to the question! To sum up, in this case, can I determine the equivalent capacity by the following?
$$C_{eq, x\to y}=\frac{q_1+q_4}{V_x-V_y}=\frac{q_3+q_5}{V_x-V_y}$$
And can I evaluate the charges I need (e.g. ##q_1## and ##q_4## ) by using mesh...
Thanks for your answer and the clear picture! I'm also learning how to use KVL properly, nevertheless I asked just because of the equivalent capacitance of the system between points ##x## and ##y##.
Suppose that, using KVL, I find out ##V_x-V_y##. Then how do I calculate ##C_{EQUIVALENT \, x...
Homework Statement
Calculate the equivalent capacity of the capacitor system between points ##x## and ##y##
Homework Equations
##C=q/V##
The Attempt at a Solution
I'm asking about this problem because I know how to calculate ##V_x-V_y##, but I don't know how can I extract the equivalent...
Thanks a lot for your answers and your help!
I still do not really get if statements like the one in my question are somehow true or not... The remainder is bigger where ##f''(\zeta)## (the second derivative) is bigger, and there the approximation is worse. But here for istance, I understand...
I studied Taylor series but I would like to have an answer to a doubt that I have. Suppose I have ##f(x)=e^{-x}##. Sometimes I've heard things like: "the exponential curve can be locally approximated by a line, furthermore in this particular region it is not very sharp so the approximation is...
Thanks a lot for your kind help!
The only possible equation in the link relating these variables is $$v=\sqrt{\frac{T}{\mu}}=\sqrt{\frac{T}{m_{rope}/L}}$$ I rewrite the two conditions I have
$$f_1 \cdot 2 L=v_1=\sqrt{\frac{T_1}{\mu}}=\sqrt{\frac{T_1}{m_{rope}/L}}\tag{1}$$
$$f_2 \cdot...
Thanks again for the answer! Knowing ##\mu## allows me to get ##L## once I know ##m_{rope}##.
But getting ##m_{rope}## is still a problem, as ##m_{rope}## has nothing to do with the mass of the object ##m##, its volume ##V## or its density ##\rho##.. So it is still an indipendent variable..
I...
Thanks a lot for the reply!
I read all the link and formulas but I fail to see the piece of information I did not use. After all here I have 3 indipendent unknown
Lenght of (horizontal part of) the rope ##L##
Density of the object ##\rho##
Mass of the object ##m## or, equivalently its volume...
Thanks for the answer!
Having the wavelenght would solve the problem because ##\lambda_1=\lambda_2=2L##, the problem is that I cannot have ##v_1## and ##v_2## but only the ratio $$\frac{v_2}{v_1}=\sqrt{\frac{T_2}{T_1}}$$ Which I already used to determine ##\rho##.
Is there another condition I...
Homework Statement
A rope has an end fixed and the other is passing through a pulley and has a body attached to it. The fondamental frequency of the rope is initially ##f_1=400 Hz##. If the body is then put in water the fondamental frequency of the rope becomes ##f_2=345 Hz##. If the linear...
Thanks a lot for the answer!
For part b)
The pressure on the vapor equals the (constant) pressure due to weight of the piston ##p=\frac{(9.81 m/s^2 \cdot 3 kg)}{\pi r^2}##
$$P=\frac{dV}{dt} \frac{c_p}{R} p$$
Here I used the fact that, in isobaric process the heat can be written as##Q=n c_p...
Homework Statement
Consider a cylindrical tank closed by a movable piston with mass ##m=3 kg##. The radius of the cyclinder is ##r=7.5 cm##. In the tank there is a mass ##m'=2 kg## o water at temperature just below ##100°C##. At the base of the cyclindrical tank there is an electrical heater...
Homework Statement
Homework Equations
Fluid in rotation
The Attempt at a Solution
This exercise is quite different from the classic one of fluidi in rotation. Before rotation starts the height in one branch is bigger than in the other, so I do not really know how to approach the problem...
Homework Statement
Two infinite ropes, rope 1 and rope 2, of same linear density ##\mu=0.1 kg/m## have the same tension ##T=100N## and lie on the same plane, one perpendicular to the other. The two ropes are connected in the origin. On one of the two branches of rope 1 an harmonic wave is...
Thanks so much for the reply!
Taking the projection of ##v_A## on ##v_S## gives the correct result! The two ways looks quite equivalent, the only thing I could think of is this
If I set ##v_{A,projection}=v_{S}## this means that ##v_{A}>v_{S}## (supersonic speed)
If I set...
I would like to be sure about one case of the use of Doppler effect with sound waves.
If the medium (in the case of sound air) is moving, but there is no relative motion between the observer and the source there is no Doppler effect at all. (And the absence of relative motion is...
@The Bill
I thought again about the problem, but still seems that the right expression is the opposite of the one in the solution.. If I may ask, would you be so kind as to give me some further suggestions on why what I tried is wrong?
Thanks a lot again for your help
Thanks a lot for the reply! I thought about the problem again but still have some unclear points.
The physical definition of ##A## is the distance between the poisition of equilibrium and maximum excursion of the rope. That means that ##A##, as amplitude, is necessarily positive. Is this...
I came up with a basic doubt on heat exchange. Consider this example situation.
A cube of ice of mass ##m## and at temperature ##\theta <0°C## is put in contact with a resevoir exactly at the temperature ##T=0°C##.
The question is: does the ice melts, i.e. does the ice pass to liquid state? Or...
Thanks a lot for the answer!
Don't want to find an exception to the rule! :biggrin: But I found these two cycles in two exercises and I wondered how to behave in this case. My only worry is (and I suppose the answer is yes):
In any "clockwise" cycle is the work done by gas positve? (And...
Thanks for the reply! I made a stupid example. If I got your point the cycle with A->B isochoric, B->C adiabatic and C->A adiabatic cannot exist. I looked for the reason of this and effectly in the case I proposed ##\Delta S_{universe}=\Delta S_{environment}=\Delta S_{environment, A->B}<0##...
Thanks for the reply! But this is in constrast with the fact that, in any cycle, since ##\Delta U=0## we have ##Q=W##, and in this case ##Q## is only the heat in the isochoric process, which is positive and this leads to ##W>0## necessarily.
Consider an ideal gas following a thermodynamics cycle, represented on a ##P-V## plane. I read that if the cycle is "travelled" clockwise then ##W_{gas, cycle}>0## so the gas does positive work, while if the cycle is "travelled" counterclockwise then ##W_{gas, cycle}<0## but it seems to me that...
I'm confused on the efficiency of a Thermal engine in the case it is reversible or not reversible, in particular where the ideal gas follows isochoric or isobaric processes.
Infact during isochoric and isobaric processes $$Q_{isochoric}=n c_v \Delta T$$
$$Q_{isobaric}=n c_p \Delta T$$
So the...
The thermal engine efficiency is defined as
$$\eta = \frac{W_{\mathrm{produced}}}{Q_{\mathrm{absorbed}}}\tag{1}$$
A more general definition of efficiency (not only for thermal machines is) $$\eta = \frac{\mathrm{Work \, produced}}{\mathrm{Energy \, absorbed}}\tag{2}$$
But suppose that, in one...
Thanks for the reply! I'm a little in late! Yes I translated literaly.. I'm quite sure it is asking to consider the same process of point a) and b) but in the case that process is reversible (in fact the heat exchanges are infinitesimal) and calculate the mass of water present at equilibrium...
I'm a bit confused about the following situation. In a irreversible thermodynamics process the molar heat of an ideal gas changes according to a function of the temperature, say ##c_v=f(T)## (which also leads to ##c_p=R+f(T)##) and I'm asked to determine the heat exchanged during that process...
In a adiabatic process (not necessarily reversible) from ##V_a## to ##V_b## the work can be written as $$W=\frac{p_aV_a-p_bV_b}{\gamma-1}$$ Where ##\gamma= \frac{c_p}{c_v}##
Suppose that the adiabatic process in question (again, not necessarily reversible, so ##pV^{\gamma}## can also not be...
Homework Statement
A cylindrical glass tube (linear thermal expansion coefficient ##\alpha##) contains liquid (volume thermal expansion coefficient ##\beta##). The height of the tube is ##h_{t,0}## and the height of the liquid inside of it is ##h_{l,0}##. If the temperature changes of an amount...
Homework Statement
A source emits a spherical sound wave at frequency ##f=110Hz## with power ##P=1 W## in a solid angle of ##2 \pi sr##. An observer moves with velocity ##v_{oss}=108 km/h## towards the source. Determine the sound intensity level received by the moving observer.
Homework...
Thanks a lot for the suggestions!
The projection of ##\vec{v_s}## is $$v_{s,x}=v_s \frac{x}{2 \sqrt{D^2+(\frac{x}{2})^2}}$$
Unfortunately I can't see the point still, if I set ##v_{s,x}## equal to ##v_A## I get what I tried to answer in the first post which does not agree with the answer given...
Homework Statement
A source emits a very brief sound signal. A receiver ##A## moves along the ##x## axis with a varying velocity such that it receives constantly the echo from the reflecting wall. Find ##v_A## as a function of the position ##x##, knowing the distance ##D## and the speed of...
How are the intensity of a sound wave and the Doppler shift of frequency related togheter?
That is, if the source or the observer are in relative motion, how does the intensity change?
For a sound wave $$I=\frac{1}{2} \rho \omega^2 A^2 c=2 \pi^2 \rho f^2 A^2c$$
(##c## is sound speed, ##\rho##...
I'm facing some difficulties in using "boundary conditions" in a simple wavefunction.
The wavefunction I'm considering is $$\xi(x,t)=A sin (k x \pm \omega t +\psi)$$
The minus or plus are for progressive or regressive waves. The indipendent parameters are 4: ##A##, ##k##, ##\omega##, ##\psi##...
Homework Statement
A sinusoidal wave on a rope with linear density ##\mu=0.012 kg/m## is described in SI units by $$\xi(x,t)=A sin (kx-\omega t)= 0.15sin(0.8x-50t)$$
a) find the maximum acceleration of a rope element
b) find the maximum transverse force on a piece of rope ##1 cm## long
c) Show...
I'm currently doing my Bachelor of Physics in Italy, my projects for the future are to apply for a MSc in Physics in some good European universities in Germany or in the UK. (Just to say, I was thinking about München or London).
Unfortunately I'm not sure I will be able to end my studies in the...
Thanks for the reply! So in this case, ##Q=0## and ##W_{fan}=\Delta U##? (Or equivalently ##-W_{gas}=\Delta U##, since ##W_{fan}=-W_{gas}##)
But that's look more like an adiabatic process.. Effectly the tank is isolated so the process is also adiabatic, beside isochoric..
In conclusion, if I...
I came up with a doubt regarding isochoric irreversible processes. Is it always true that, for any isochoric process, reversible or not, the work exchanged by the system is zero and the heat exchanged is ##Q=\Delta U##?
I'm asking this because, in a exercise on thermodynamics trasformations of...
Thanks for the answer, part c) is the same of a) (find the mass of the water present in Equilibrium conditions) but in the hypotesis of reversible process.
For part a) I did the following
Since the ##|m_W c_W (0°C-T_W)|> m_I c_I (0°-T_I)## ice melts but, since ##|m_W c_W (0°C-T_W)| - m_I c_I...
Homework Statement
In an adiabatic container are placed , in rapid succession , a mass of ice , ##m_I= 2 kg## , at temperature ##T_I = -10 ◦C## and a mass of water , ##m_W = 1 kg## , at the temperature ##T_W = + 20 ◦C## . Determine :
a) the total mass of water present in the container at...
Homework Statement
The tank in picture has section ##S_1## and it's linked with a tube of section ##S_2=\frac{1}{\sqrt{17}} S_1##. The tank is filled at an height ##h## and this level is kept constant by a sink ##R##, in such way that the exiting volumetric flow rate is ##Q=0.3 m^3/s## and...
Homework Statement
You have a device that can measure sound waves only if the frequency of the wave is in the range ##0.8 kHz- 20 kHz##. You have a whistle that produces sound waves at ##21.5kHz##. You ride a bike moving away from a wall, at the same time you blow the whistle and hold the...
The beats frequency heard from the interference of two sound waves with frequencies ##f_1## and ##f_2## is $$\nu=|f_1-f_2|$$
Nevertheless the frequency of the resulting wave is not ##\nu## but the mean value of the two frequencies
$$f_{resulting}=\frac{f_1+f_2}{2}$$
As far as I understood...
Thanks a lot to both for your suggestions!
So actually both the block and the fluid do move.. Since my aim is to find the variation of fluid level I tried to interpret the phenomenon of case 1 as described by my answer in the question, now that I know that the block moves too. I made a drawing...
Thanks a lot for your help! I would say that the relation is ##\vec{F}_{Archimedes}= \vec{F}_{net}= \vec{F}_{up} + \vec{F}_W##, so, if this is right, then I can get what I'm looking for, ##\vec{F}_W##, as ##\vec{F}_W=\vec{F}_{net}-\vec{F}_{up}=\rho_W V g - \rho_W g L \pi R_1^2##.
But in the...
Ok! Well in that case the pressure would act above, on the sides and below the tank and the resulting force would be the bouyant force I guess
The problem here is that the pressure is acting only above and on the sides and I cannot see the way to calculate the force..
Thanks for the answer! Yes it acts as a suction cup. But there surely is a force exerted on the tank because of the water above it and that's the pressure force I would like to know. Is the expression ##F_p= \rho_W g L \pi R_1^2## correct in this case?
Homework Statement
Consider the truncated cone tank submerged in water: inside the truncated cone tank there is air. Evaluate the forces acting on the truncated cone tank.
Homework Equations
The Attempt at a Solution
The forces are the following
Boyuant force : $$F_b= \rho_w g V_{tank}$$...
Homework Statement
I'm confused about the following kind of situation. Consider a block of density ##\rho_b##, mass ##M_b## and section ##S_b## that floats on a liquid of density ##\rho_l##, in a tank of section ##\mathcal{S}##. On the block there are some objects (all equal), of density...