Thanks for the interesting info. This is useful. I'll check out the book by Schoenfeld. I am a mechanical engineering major. I had a short stint as a research scholar in a dept of theoretical physics, but I dropped out after two years. I currently coach students of my town for math and physics...
My apologies. I did look at various forums to decide where this belongs, but most of the threads on academic guidance forums seemed to be on courses and specific topics, and not studying in general. But now I see there are posts on 'learning' as well. I also wondered whether I should post it in...
Thanks.
Just to be clear, I am not asking for shortcuts to study physics without any hard work. I am looking for tips for more efficient learning, which is why I gave the examples above. I have noticed that different students, who seem to put in the same amount of effort, end up with different...
I can find several resources (in this forum and elsewhere) on pedagogy and teaching tips that are geared towards teachers. Are there any books or resources that provides tips for students of physics, that would make learning more efficient and effective?
Examples of the kind of things I am...
Thanks. I get that it matches the observed speed of sound. I am just curious as to why? Was there a way we could have guessed beforehand that it would work?
How do we know that this case satisfies that condition? Is there a practical limit below which a process can be reasonably assumed to be quasistatic? I have read that we can make the quasistatic approximation for expansion and compression processes, if the boundaries are moving much slower than...
The speed of sound in a gas at temperature T is given to be ## v=\sqrt{\frac{\gamma RT}{M}}##, where ##\gamma## is the adiabatic exponent, R is the gas constant and M is the molar mass of the gas. In deriving this expression, we assumed that the compression and expansion processes were so fast...
I see. So if I assumed du and dv to be positive in the first two terms, then they must remain positive in the last term. So the negative sign remains negative. In general, if the numbers were different, and if I want to do it the first way, to find the maximum error, should I try different...
If I write ##f=\frac{uv}{u+v}## and then take differentials on both sides, I get ##\frac{df}{f}=\frac{du}{u}+\frac{dv}{v}+\frac{du+dv}{u+v}##, I get the fractional error as 0.03. (I have replaced the negative signs that come as a result of quotient rule with positive signs, since we are asked to...
Thank you. That makes complete sense. Having a magnitude and direction is an intuitive way of thinking about certain vector quantities we encounter in high school physics, but is not the definition of a vector. And it isn't even the best way to describe vectors even in physics. How would you...
I agree that it is indeed a misapplication. I used it as an example of a misapplication. I was trying to show that even though velocity is a vector, adding velocities of two different objects does not make sense, even though you can in principle add two vectors. Please note the sentence, 'But...
Well, I did make an attempt to answer the question: The resultant temperature when you mix two substance is not what 'adding temperatures' means.
I thought the above example must be convincing.
Moreover, the description I gave of vectors and scalars are not my own, but from the prescribed...
The students actually did know through intuition that temperature, upon mixing, should NOT just add up. Their question was, since we know that they just don't add up like masses do, how can we still call them scalars.
I am trying to describe vector and scalar physical quantities, without defining vectors and scalars mathematically.
I think I understand. We are mapping on physical quantities to the abstract concept of vectors. So we can perform whatever operations are defined on vector spaces on these...
I understand. I know about heat capacity, but this is a question asked by students when discussing vectors and scalars. And I gave them the example of person in Africa and U.S. displacement that I mentioned in the original post, to show that one could blindly add two quantities as vectors or...
So it is in terms change in temperature, that we can talk of addition : T+ΔT, where T=300 K and ΔT= 30 K would only give 330K ,and nothing else. That is good. Thanks.
There is a small issue of decrease in temperature though. Distances, which are scalars, only increase and never decrease during...
I was going through vector and scalar quantities (the way they are taught in high school), and this is how I think students are supposed to understand it:
Scalar quantities are quantities that add like numbers. For e.g. Mass. If I add 100 g of water to a bucket and then add a further 100 g, I...
In the first case, they would meet at the midpoint again.
In the 2nd case, if say the pulse was initially at a distance d from one boundary, then after an even no. of reflections, they will meet at the same initial position of the pulse. After an odd no. of reflections, they will meet at a...
Assuming there are no losses (Reflection coefficient is 1), they are inverted and reflected. Shape and size of the pulses remains the same, propagation speed remains the same (since it is a property of the medium). So the pulses just bounce about, inverting at each reflection. And whenever and...
Homework Statement
A horizontal string at tension T is tapped at the midpoint to create a small transverse pulse. What happens to the pulse as time passes? If the pulse is instead created at a point other than the midpoint, what happens to it? Neglect damping.
Homework Equations
Speed of...
Strange things will happen in case we stick to the perfectly elastic material model. if we push one end of the rod with v=c, it will reach where the other end is, even before the other end starts to move. So the rod is effectively reduced to zero volume. (If v>c, I can't even imagine!) Of...
Ah. Thanks. Lateral deformation makes sense. The simulation was interesting. In the opposite process of pulling (extension), what will happen? Will the object certainly break?
Consider an elastic rod lying on a table. If one end of the rod is pulled/pushed along the length of the rod with speed v, the other end will not immediately start moving, because any disturbance takes time to propagate along the rod. To be precise, the other end will move after a time t=L/c...
It does, doesn't it ? Intensity depends on the amplitude and the wave velocity, which is the same for the two components.
When you say 'the two waves', do you mean the two sinusoidal components of the 2nd wave? This is what I thought you meant. Or do you mean the pure sinusoidal wave vs the...
Thank you.
For the original wave,
n_p= \frac{c \times \frac{1}{2} \epsilon _0 {E_0}^2}{\hbar \omega}
For the compound wave , no. of photons with energy ħω
n_{p,\omega}= \frac{c \times \frac{1}{2} \epsilon _0 {E_0}^2}{\hbar \omega}
and no. of photons with energy 2ħω
n_{p,2 \omega}= \frac{c...
Homework Statement
In a photoelectric effect experiment, a monochromatic plane wave of light falls on a metal plate. The electric field in the light wave at a point near the plate varies according to E=E_0 \cos (\omega t). This results in a saturation current of 6 μA. If instead, the light wave...
I came across this book 'Street fighting Mathematics, The art of educated guessing and opportunistic problem solving' , by Sanjoy Mahaan, published by MIT press. The book talks about how we can guess some property of the solutions of a number of physics and math problems without actually solving...
Well, you seem to have a problem with the whole of thermodynamics as such. And your concern, it seems, is that it is impractical. Now, I am no expert , but I see around me engines, air conditioners and refrigerators, all working fine. Of course, ideal gas and quasistatic process etc are...
Sorry, not a text, a problem book. 'Advanced Problems in school physics', by cengage publication. I think it is out of publication. Problems compiled by indian authors , I think mostly physics olympiad problems.
Awesome! Thanks.
I was considering the extreme case of a point on the edge of the half pipe, on which the plate seems to subtend zero angle. I guess as a limit, it would still subtend pi/2.
Depends on the point we choose. For eg at a point adjacent to the plate it subtends zero angle.
The farthest point does subtend pi/2. If that was true for all points, then great. But that,s not true for all points, is it?
Homework Statement
(This is not a HW problem, but HW-type problem.)
A half cylinder of radius R and length L>>R is formed by cutting a cylindrical pipe made of an insulating material along a plane containing its axis. The rectangular base of the half cylinder is closed by a dielectric plate of...
Well what if you slowly change the external pressure from P1 to P2 while holding the piston fixed and then release the piston? That is effectively the same problem.
I think so. When they are moving together after the collision, there is no acceleration (assuming friction is absent). So Newtons laws would tell you force on each mass should be zero.
I got it. We can use equation of state for an ideal gas. Assuming the process is quasi-static, both initial and final states will be equilibrium states. Then
P_1 V_1 / T_1=P_2 V_2/ T_2 \\
\implies T_2=( \frac{V_2}{V_1}) (\frac{P_2}{P_1}) T_1 \\
\implies T_2=2(\frac{p_0 A+m g}{p_0 A+\rho g h...
Thanks, I understand. I got half the answer. A number of hasty mistakes on my part in the attempt above. The process isn't adiabatic. It isn't given whether the gas is mono or diatomic, so we don't know γ.
At any instant of time, external pressure on the gas is Pext=P0+ρgy+mg/A, where y is the...
MODERATOR'S NOTE: Moved from other forum, so no template
@Chestermiller
I am still having trouble figuring out if a given process is Quasi-static or not.
Consider the following case. The cylinder consists of an ideal gas at the bottom and a liquid of density ρ at the top separated by a piston...
Thanks a lot. That cleared a lot of my confusion. So the process is not really isobaric, even though external pressure is constant during the compression. We can't even talk about the 'pressure of the gas' during the process of the compression because it doesn't take a single value. So basically...
Ok. So if I understand correctly, the process is adiabatic, but PVγ=constant is not valid because it isn't an eqbm process. Thanks.
SO is the formula valid only if the pressure is increased gradually? If I have an equilibrium process which is adiabatic and also constant pressure, then T and V...
Consider the following problem:
Gaseous helium (assumed ideal) filled in a horizontal cylindrical vessel is separated from its surroundings by a massless piston. Both piston and cylinder are thermally insulating. The ambient pressure is suddenly tripled without changing the ambient temperature...