Volume Definition and 1000 Threads

I'm wondering if there is a way to find the proper volume of the warped region of the Alcubierre spacetime for a constant ##t## hypersurface. I can do a coordinate transformation ##t=τ+G(x)##, where ##G(x)=\int \frac{-vf}{1-v^2f^2}dx##. This eliminates the diagonal and makes it so that the...

Using the equation above, I plugged in 5.5 inches for the radiu and 0.5 inches for the value of dr and then solved for the estimate of the change in volume, dV. However, the solution instead uses a value of 6 inches for the radius receiving a different estimate for the problem than I did. Is my...

I'm getting the wrong results when using an old, undocumented code and just realized there's a number lurking in it that I can't account for. It's: 0.023901488 and it is multiplied with molar volume and pressure. I have searched for a couple of hours but just can't figure out what the units...

[FONT=times new roman]Problem statement :[FONT=times new roman] I draw the problem statement above. I hope I am correct in inferring that the bowl is hemispherical. Attempt : I could not attempt to the solve the problem. We are given that the rate of change (decrease) in volume is proportional...

In Vanderlinde page 171-172, the author derives the vector potential for the magnetic dipole (and free currents) \begin{align} \vec{A}(\vec{r}) &=\frac{\mu_{0}}{4 \pi} \int_{\tau} \frac{\vec{J}\left(\vec{r}^{\prime}\right) d^{3}...

So, let's assumed ##v_i = (v_i \pm \Delta v_i)##. We can say that, for minimum values, $$\Delta X_i \Delta v_i = \hbar / (2m)$$. $$\Delta X_i = \frac{\hbar}{2 m \Delta v_i} \implies V_{min} = \Delta X \Delta Y \Delta Z = \frac{\hbar}{2 \Delta v_x m } \frac{\hbar}{2 \Delta v_y m} \frac{\hbar}{2...

I am looking for an equation that I can use to compute L/min or mL/min for a 480cc vessel going from 150bar to 250bar with a fill time of 6min. Sensors for flow rate at these pressures are hard to find, but I thought there might be a way to work this out with the parameters known. An equation...

This was a trivial question I had (which I posted here on the PF EM Forum: https://www.physicsforums.com/threads/bound-charges-polarisation-of-a-half-cone.1015308/). As I received no response on the above link I decided to post the same as a self formulated HW problem. Below I have attached an...

Let the radius of the small sphere = r 3r = 1 → r = 1/3 ##x=\sqrt{4r^2-r^2}=r\sqrt{3}## Volume of pyramid: $$=\frac{1}{3} \times (2r\sqrt{3})^2 \times r$$ $$=\frac{4}{27}$$ So m + n = 31, but the answer is 29. I guess my mistake is assuming line AB is tangent to the top sphere. How to do...

My attempt : ## \displaystyle\int_0^2 \displaystyle\int_0^{2-x} (2-2x -2y) dy dx = -\frac43 ## But it is wrong.

this formula in the picture is the average electrostatic field over a spherical volume of radius R. It is the same expression of the electrostatic field, at the (position) of the point charge, of a volume of charge of uniform density whole entire charge is equal to (negative)q. My question is...

Result My attempt

I was reading a Chemistry book when I read about the three states of matter. Everyone knows what they are, but I didn't know the simplest way to describe each of the three until I read this book. It said that a solid has a shape and a volume, a liquid has no shape but has a volume, and a gas has...

When we compute the stress energy momentum tensor ## T_{\mu\nu} ##, it has units of energy density. If, therefore, we know the total energy ##E## of the system described by ## T_{\mu\nu} ##, can we compute the volume of the system from ## V = E/T_{00}##? If it holds, I would assume this would...

Hi, Originally, the absolute temperature was thought to be around -273 Celsius around 1750 and it was the result extrapolation of of ideal gas law as shown below. I find it hard to phrase my question. But the question is how come they were so confident that the relationship between the volume...

Hi guys, M can then be split up into 2 components: the mass of the payload which is known, and the mass of the wing. The wing material has a known thickness and density meaning its mass is given by: surface area of wing* mass per m^2 (mass m^2 is used as density and thickness are known so an...

First, I tried to find the equation of line passing through (2, 0) and (0, 3) and I got ##y=3-\frac{3}{2}x## Then I set up equation for the area of one slice, ##A(x)## $$A(x)=\frac{1}{2} \pi r^2$$ $$=\frac{1}{2} \pi \left( \frac{1}{2}y\right)^2$$ $$=\frac{1}{2} \pi...

Am refreshing on this; see attached below ok we can also use the form ##[i×j=k, k×i=j , j×k=i]## right? to give us say, ##w⋅(u ×v)=v⋅(w ×u)## in realizing same solution.

Hello, I am trying to figure out the right way to approach this. First of all, other than the different Bohr radius value, does the change to a negative pion make any other difference to calculating the probability? Also what would be the correct way to apply the "small volume"? What I'm...

Find the question below; This is a textbook question and i noted that their solution of, $$A=\left[\dfrac{1}{2}×3×4×6\right]cm^3$$ is not correct in my opinion as the base is not a right angle. The base can be analysed as a rhombus and the exercise therefore is to find the related angles and...

$$V=πr^2h$$ $$V=πr^2(6-r)$$ $$\frac {dV}{dr}=12πr-3πr^2$$ For max/min value, $$\frac {dV}{dr}=0$$ $$12πr-3πr^2=0$$ $$3πr(4-r)=0$$ ##r=0## or ##r=4## $$⇒V_{max}= 32π$$ $$⇒V_{min}= 0$$, I do not think there is another way of doing...

I know that as the concentration of substrate increases, the enzyme activity increases because there are more substrate molecules to react on (but at an increasingly slower rate). Would the same reasoning work with volume? Thanks!

Pending

I found this problem, which I thought was interesting and somewhat original: Calculate the volume of the solid of revolution of the area between the line ##y = x## and the parabola ##y = x^2## from ##x = 0## to ##x = 1## when rotated about the axis ##y = x##.

In my first attempt, I started off converting the radii of all three sections from centimeters (10, 8, 6) to meters (0.10 , 0.08 , 0.06), then used the VFR=Av formula to find the speed/velocity of section one. VFR== 0.063 m^3/s A== pi*r^2=pi*(10cm)^2=pi*(0.10)^2=pi*0.01 == 0.031415927 VFR/A=v...

Since the density is 1320 g/L then for every L of solution there is 320 grams of solute. 320 is 35% of 900 hence the statement it is is a (about) a 40% solution So the volume that would have 12.5 grams would be 12.5/320 L = .039 L = 39 mL

[I've solved b, but can't figure out a for the life of me. I have a couple of attempts, but it's just nonsense, it's like I've short circuited.]

Hi, I am trying to think how to make a DYI volume knob to control variable actions on my audio card. But I don’t want one with buttons to toggle the actions.. instead I want to make one with a touch sensitive lcd screen and make the scroll knob (a físicas one) around the screen bc I want to use...

Hi, here is my attempt... Feel free to correct me if I am doing it wrong. v1 = .8 m3 p1 = 250 or 250000 n/m2 p2 = 7000 or 7000000 n/m2 Cp = 1010 Cv = 7321. isothermally p1v1 = p2v2 [Boyle equality law (isothermal process)] 250 000 * .8 = 7000000 * v2 7000000 * v2 = 250 000 * .8...

Another question about the use of the micro-canonical ensemble in deriving distributions. On the Wikipedia-page the authors mention that the total volume of the system has to be constant. See...

This doubt is confusing to me. I know it's something to do with conductors and insulators, but cannot explain. Conductors have mobile/free electrons unlike insulators. Having free electrons doesn't seem to explain this difference of charge distributions.

I have done this question and gotten: Vmin = 4pi/3(19.18)^3=29555.2 V = 4pi/3(19.31)^3=30160.3 Vmax = 4pi/3(19.44)^3=30773.5 Uncertainty: {[30773.5-29555.2]/30160.3}x100=4.04% however this is wrong... Could someone please help me find out where I went wrong, or tell me if I went the wrong...

This is not actually a homework problem. I'm old but having trouble with something that's probably at student level because it's so long since I learned this stuff. I would be grateful if someone would please take pity on me and help me out! I am trying to calculate something that includes...

Hey! :giggle: We have the set $M=\{(x,y,z)\in \mathbb{R}^3 : x^2+y^2-z^2\leq 1, \ 0 \leq z\leq 3\}$. Draw $M$ and calculate the volume of $M$. I have done the following : \begin{equation*}\int_M\, dV=\int\int\int\, dx\, dy\, dy\end{equation*} Which are the boundaries of the integrals? Do we...

Hi! I read this definition of Stellar Parallax "It is expressed quantitatively by one-half the angle subtended by the Earth's diameter E1E2 perpendicular to the line joining the star and the sun (see Fig. 2-10)." (Source Alonso and Finn: Volume 1). But, I was unable to understand how they...

Has the advent of computer trading greatly increased the size of statistics for trading volume? - or do those statistics (for individual stocks) somehow omit the flash trades done by computers? In the pre-computer days, there were people who had theories of stock trading based on both the...

What is the definition of volume inside a black hole? we know the grr element of Schwarzschild metric is negative inside event horizon, so how to define a volume inside event horizon? if there is no definition of volume, is there the definition of density?

how to find volume and surface area of this without using the upper lid

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I’m pretty sure that the force on the sphere by the wall and plane has to equal mg so the sum of the normal force is steered by the wall and plane has to equal mg. I’m not sure where to go after this. Is mg the answer or is there something I’m missing?Here is Fig: 4-31:

I sketched this out. With the z=0 and y=0 boundaries, we are looking at ##z \geq 0## and ##y \geq 0## I believe ##0 \leq x \leq 5## because of the boundary of ##y=\sqrt{25-x^2}##. This is my region ##\int_0^5 \int_0^\sqrt{25-x^2} x \, dydx ## ## =\int_0^5 xy \vert_{0}^{\sqrt{25-x^2}} \, dx##...

Solution attempt : Option : I am sure that my work is wrong. But, I must add solution attempt in PF that's why I just added that. How can I solve the problem?

Air displacement plethysmography I saw a tv programme many years ago which shows this method of measuring the volume of a patient's body. Air displacement plethysmography was a procedure that I saw being used and, tbh, I never asked myself how it works, until now. It's smart, imo. You put...

I'm trying to do the math for a backyard thermodynamic pump experiment, and getting stuck. Suppose an empty 3.79 liter container was airlocked by a vertical 25 cm long empty tube whose end sits at the top of an unlimited supply of water in a basin. The tube protrudes through the container such...

Summary:: Gibbs and Helmholtz energies calculations for heating an ideal gas at constant volume I am solving a problem involving an ideal gas that undergoes several chained changes of state. One of the steps asks to calculate the change in Gibbs Energy (DeltaG) and Helmholtz energy (Delta A)...

https://physics.csuchico.edu/~eayars/publications/AJP00961.pdf http://www.phys.utk.edu/demoroom/MECH/The%20Vacuum%20Canon.pdfSo I get the outside atmosphere is what provides air density and such in the pdf above^. However, why is it that most cannon demonstrations use just the air from the...

I imagine the shape will be like this: and I need to find the volume of the shaded part. I am planning to use: ##V=\int A(y) dy## I tried to take the cross-sectional area A(y) to be triangle: and the base of the cylinder to be: So it means that the base of the triangle will fulfill the...

The gold pavilion in the city of Kyoto is covered with gold leaf. Gold leaf has a thickness of 100 nm (nanometres) and is made from gold bars. A gold bar has a volume of 0.65 dm^3. How many square metres can the gold leaf from a gold bar cover?

I’m trying to calculate how many Joules are stored in the Hyperion tree, the worlds tallest (115.84 m). However, I cannot find the mass of said tree, and am trying to find it by multiplying density by the volume (530 m^3) because if p=m/V then p•V=m, but I cannot find the density of the tree, so...