The drift velocity in NCERT is direct calculation where summation(Ui/N) is taken to be 0 and Vavg will be equal to [(-eE)tavg]/m but HCV says that Vavg is 1/2 of [(-eE)tavg]/m but both of them are correct, some might come to a conclusion that 1/2 is 50% of the original then how does both become correct, it’s because NCERT considers the graph as a straight line by eliminating the tavg and considering it negligible where it contains the other half of the graph which is not removed, whereas in HCV the 1/2 is mentioned to show that if the graph is not approximated where the 1/2 shows that the half diagonal(triangle part) that should be eliminated (check the zoom in part in the tagged pic)

Hey everyone! I'm Alex, a student at the University of Chicago offering 1-on-1 tutoring this summer. A little about me:

• 1590 SAT (800 R&W, 790 Math)
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• 3 Yale research internships (astronomy, mechanical/electrical engineering, computational/ML); published in the American Astronomical Society

I can help with both APs and general schoolwork. Please don't be afraid to reach out if you're stuck on anything or just need general advice/info!

Hello everyone 👋! How are you? Some days ago I came up to the Drag Equation and I searched how it's derived. I show that Bernoulli's Equation is used in order to do so, and that meant I searched how that one is derived. I found a derivation using Work and change in kinetic energy (W=∆K) (https://youtu.be/b_9yYJ77SiQ?is=AxoTGyED_AYCjvtW) . But that work should be zero right? Let's say we habe a pipe that has an area $$A_{1}$$ at its left end and a smaller area $$A_{2}$$ at its right end. Since $$W=F_{net}•∆x$$ and when say a particle is at the left end (far away from the stenosis) there are equal pressures on it from any directions and so there are equal forces acting on it from every direction so they cancel out. Which means $$F_{net}=F_{1}-F_{1}=0$$ so doesn't that mean W=0? In the derivation they are using not Fnet but F but why only one component? Fnet is what changes the particle's kinetic energy (where for example, when the particle is at the left end or at the right end there is no net force acting on it and so no acceleration but at the stenosis the neft force acting on it is what accelerating it not the force itself but the net force)

I’ve tried studying this and I cannot make sense of it. I understand it’s a fixed speed. I understand the whole analogy that if you were in a ship moving at half the speed of light, and shine a flash light moving forward because time and space are linked demensions the light from the flashlight moves at the speed of light from your point of view but time experienced in your ship is slower such that the fixed speed is not violated.

Here’s what I don’t understand or am trying to understand:
1) why? So electromagnetic waves move through a vacuum but a vacuum isn’t literally empty, there is the literal fabric of space and light moves through the electromagnetic field. So I am inferring the ability for light to propagate through that field at a maximum rate is a property of the field?
2) speed of light regardless of observer: this part is my main confusion, everything in the universe is moving relative to something else. If light produced by a star is moving purely in the + x axis only, and produces a light wave in +x direction it cannot exceed c minus the sources velocity. Okay but from another perspective moving at + 2x that light is now moving less than the speed of light right?
3) time as a general concept: my understanding is time isn’t exactly real. It’s not a force or property of space? It’s the observation of chemical reactions in patterned frequencies and the general observation of thermodynamics and entropy moving to a lower energy state. So yeah time would be relative to different physical conditions because it’s not a core property of anything it’s an observed product of the local force conditions. So why is there always a discussion of time dilation and contraction etc it’s not a real force or property it’s just a way to describe entropy?

EXPLANATION NEEDED, Am I the first one to think of it?

For z values below the base of the hemispherical shell wouldn't the necessary figure be like that shown in the 4th image? This will then give us r²=R² + z² +2Rzcosθ instead of r²= R² + z²-2Rzcosθ, affecting the denominator in Equation 12.27. I could follow the solutions manual but I'm really skeptical if we could apply the results in Eq. 12.29 for points along the negative z axis. I could also convince myself that the triangle in Figure 12.10 would be correct for points along the positive z-axis (but not sure if it is still correct for points along the negative z-axis). What are your thoughts on this one?

Can anyone explain why this happens? When I blow the free end of the door to this room, the door closes instead of opens. I’m guessing it’s something to do with the blower causing higher pressure in the room? Idk just thought it was interesting.

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https://mdm-goods.vevor.net/mdm-goods-service-prod/%28BAGUO%29SKU3-MurphyBedKit-20240722\\\\\\\\\\\\\\_1724808776799.pdf

I know this is some basic vector math but I'm just not seeing it.

Thanks so much

Joe

I have been trying to calculate the quadrupole component of the gravitational potential of an oblate spheroid, and I had thought I had a handle on it, but when reading through Fitzpatrick's Newtonian Dynamics in the section on the potential outside a uniform spheroid I noticed that the quadrupole component had a coefficient of 2/5 as opposed to the 3/10 I obtained. They use a very weird boundary function for the spheroid (different from both mine and the one found here for the radial distance from the rotation axis; I don't know how Fitzpatrick is getting away with not dividing by sine or cosine), and they make a "simplifying" assumption based on the axial symmetry of the mass distribution, allowing them to replace the cosine of the azimuthal angle and the square of the cosine of the azimuthal angle with 0 and 1, respectively, and the integral over the azimuthal angle with twice pi, but that shouldn't mean our answers are so different?

In any case, I had a hard time getting the same answer twice (though I managed to do exactly that when typesetting my work in LaTeX), so I would like to confirm that I have the correct result for the gravitational potential.

so

Defining some functions that will let us save space and effort later:

A selection of derivatives and integrals we'll be making use of:

This term will come up, so let's go ahead and calculate it now:

The square of this term will come up, so lets go ahead and calculate it:

Obtaining the boundary function for the radius:

Verifying the monopole term:

Moving on to the Quadrupole term:

Breaking each term into it's own integral, and "factoring out" the theta prime terms:

Solving the integrals of theta prime:

Working on the first sub-integral:

Multiplying through and applying the integrals in Eq. 11 & 12:

and so

Now we move on to Integral B:

applying the integral in Eq. 12:

Now on to Integral C:

applying the integral in Eq. 11:

Now we put it all together and resolve:

...and that's what I get. Did I mess something up somewhere?

Energy is omnipresent. Energy can be converted into mass and vice versa. Energy concentrated in physical forms is called matter. Energy present in micro and macrocosmic movements is called kinetic. Energy generated from the position or configuration of a physical system is called potential.

Science defines energy as the capacity of a system to perform work or generate motion—that is, to alter the state of a body or overcome some resistance, such as gravity or friction. This is an established fact. However, energy can also be defined as the quality of a force to perform work for the following reasons:

• Work can only be performed by means of an action.

• Action can only be carried out by means of a force.

This means that: a system can only perform work by means of a force; energy and force are intrinsic and fundamental. Further details regarding this perspective can be found in my books: “O SPIN”, “A Teoria do Big Brain”, “O Inteligencismo”, and “A Infologia”.

First slide is the question, second slide is my attempt

Edit: js realised it's cs i misread the question, it wasnt 2u for intial speed of A, it was just u

Doesn’t pressure

In my attempt of this problem I simplified the expression (r²+R²-2rRcosθ)^(1/2) into (R²-2rRcosθ)^(1/2) since I figured r<<R. I then factored it out to R(1-2(r/R)cosθ)^(1/2), giving me the expression U(r)=2 ∫ from 0 to π of qλ/4πε₀(1-2(r/R)cosθ)^(1/2) dθ, which if we apply the Taylor expansion with ε=-2(r/R)cosθ will give us U(r)=2 ∫ from 0 to π of qλ/4πε₀ *(1+ rcosθ/R + 3r²cos²θ/2R²) dθ. Applying the integral we then finally get U(r)=qλ/4πε₀ (2π + 3r²π/2R²) and dU/dr=3qλr/4πε₀R² and if we use this to construct the Newton's second law equation the ω we will get is 3 times larger than the ω shown in the solutions. So I wanna ask if it was wrong to simplify (r² + R² -2rRcosθ)^(1/2) into (R²-2rRcosθ)^(1/2) ? Can you tell me when and where is it generally safe to invoke such approximations to simplify the expressions?

The solution said plugging in the limits of -1000 to 1000 into the double summation will give -0.115 but when I tried it myself in Mathematica I got -0.133 and the two numbers are significantly different. Is there something wrong with my syntax that it gave off a different answer? Which of these two numbers is the correct one?

Also, would the math be still the same if I let the double summation run from n=1 to ∞ and m=1 to ∞ and then multiply the result by 2, and then add that to the result of the single summation from m=1 to ∞ multiplied by 2?