Radius Definition and 1000 Threads

Hi there, My textbook says "When a beam of high energy electrons is directed at a thin solid sample of an element, the incident electrons are diffracted by the nuclei of the atoms in the foil." What does this mean exactly? Are the atoms diffracted by the gap between different nuclei? It...

Homework Statement Derive a relationship between the speed v, of a body moving in a circle of radius r, and the frequency f, of the revolutions. Homework Equations v=2πr/T T=1/F The Attempt at a Solution Well, I thought this would be as simple as solving for F in the second...

Homework Statement A circle of maximal area is inscribed in the region bounded by the graph of y = -x^2-7x+12 and the x axis. The radius of this circle is of the form (sqrt(p) + q)/r where, p, q and r are integers and are relatively prime.What is p+q+r Homework Equations Vertex form...

Homework Statement Sodium is, to a good approximation, a monovalent free-electron metal which has the body-centred cubic structure. (a) Calculate the ratio of the Fermi wavevector to the radius of the largest sphere that can be inscribed in the first Brillouin zone. Remember that the...

What exactly is the radius of curvature of an object? And how would this be applied to a question such as the following: A glass porthole of a submerged craft has parallel curved sides, both of radius of curvature R. What would R be in order that an object in the water 2m away from the...

Homework Statement k is a positive integer. \sum^{\infty}_{n=0} \frac{(n!)^{k+2}*x^{n}}{((k+2)n)!} Homework Equations The Attempt at a Solution I have no idea.. this is too confusing. I tried the ratio test (which is the only way I know how to deal with factorials) but I get...

Two soap bubbles of radius r and R are in touch find the radius of curvature of their point of contact? (Both bubbles are touching each other with their external surfaces) I have no idea about this question. can you please try to help>

Homework Statement Two identical satellites orbit the Earth in stable orbits. One satellite orbits with a speed v at a distance r from the center of the earth. The second satellite travels at a speed that is less than v . At what distance from the center of the Earth does the second...

Hi, Suppose I have an analytic function f(z)=\sum_{n=0}^{\infty} a_n z^n the series of which I know converges in at least |z|<R_1, and I have another function g(z) which is analytically continuous with f(z) in |z|<R_2 with R_2>R_1 and the nearest singular point of g(z) is on the circle...

Hey, If initially I have some solid sphere spinning at some initial angular velocity and in its final state I have the same solid sphere spinning at a different angular velocity except some of its mass has moved to a ring 45 degrees in latitude from centre , such that this ring of mass is...

I am looking at inflation at the moment, and it says in my textbook that (aH)^(-1) is constantly increasing in matter or radiation dominated epochs. a is always positive and always increasing. This tells me that da/dt is positive. I think that setting the universe to MD/RD means that da/dt...

How fast must a plan fly in a loop-de-loop if the pilot experiences no force from either the seat or the safety belt when he is at the top of the loop? I just need to be pointed in the right direction. Thanks in advance for your help.

Homework Statement how to prove that radius of convergence of a sum of two series is greater or equal to the minimum of their individual radii i don't know how to begin, can someone give me some ideas?

A hologram with "vibrational energy" to neutralize EMF radiation within its radius? http://www.safespaceprotection.com/qanda.aspx How do the products work? Our products 'repattern' the electromagnetic field by creating a 'coherent polarizing field effect'. When the charged particles are...

Homework Statement A 1200-kg car is traveling at 10 m/s on a road such that the maximum frictional force between its tires and the road is 4000 N. The minimum turning radius of the car isHomework Equations I need the equation to solve.The Attempt at a Solution 30m?

These are my equations for the total Universe_mass-energy equivalence based upon the Lambda-CDM model parameters and the Hubble Space Telescope (HST) and WMAP observational parameters and the observable Universe radius in Systeme International units. I attempted to collapse the Lambda-CDM model...

Homework Statement Find the radius of convergence and interval of convergence of the series: as n=1 to infinity: (n(x-4)^n) / (n^3 + 1) Homework Equations convergence tests The Attempt at a Solution i tried the ratio test but i ended up getting x had to be less than 25/4 ...

Homework Statement Let A be a real nxn matrix with non-negative elements satisfying \sum_{j=0}^n a_{ij}=1. Determine the spectral radius of A. Homework Equations Denote spectral radius \varsigma(A)=max(\lambda_{i}) We know \varsigma(A) \leq ||A|| for any norm || || 3. Attempt at the solution...

A proton (q = 1.6 X 10-19 C, m = 1.67 X 10-27 kg) moving with constant velocity enters a region containing a constant magnetic field that is directed along the z-axis at (x.,y) = (0,0) as shown. The magnetic field extends for a distance D = 0.7 m in the x-direction. The proton leaves the field...

Gamma is a circle of radius 2 oriented counterclockwise. $$ \int_{\gamma}\frac{dz}{z^2+1} = \int_{\gamma} = \frac{i}{2}\left[\int_{\gamma}\frac{1}{z+i}dz-\int_{\gamma}\frac{1}{z-i}dz\right] $$ $\gamma(t) = 2e^{it}, \ \ \gamma'(t) = 2ie^{it}$ $$ \int_{\gamma}\frac{2ie^{it}}{2e^{it}+i}dz $$...

Homework Statement If f(z) = \sum an(z-z0)n has radius of convergence R > 0 and if f(z) = 0 for all z, |z - z0| < r ≤ R, show that a0 = a1 = ... = 0. Homework Equations The Attempt at a Solution I know it is a power series and because R is positive I know it converges. And if...

In this link the proton charge radius is calculated based on an experiment involving a muon and a proton http://www.sps.ch/en/artikel/progresses/muonic_hydrogen_and_the_proton_radius_puzzle_20/ It talks about "In summary, we have measured the muonic hydrogen transition at a frequency of...

When dissolved in water, which of the following ions will form stronger ion-dipole bonds with the water molecules? Li+ or Na+? Both have roughly the same charge... Na has greater radius, but I don't see why or how that has any bearing on the problem.

Homework Statement You and a friend decide to determine the radius of the Earth. You synchronize watches; then your friend drives 50km due west, at latitude 40°. Each of you determines the time when the Sun lies due south -- on the meridian Your friend observes the Sun to be on her meridian...

Homework Statement A block of mass m1=2kg is attached to a cord. The cord goes down through a hole in the table and is attached to mass m2=4 kg hanging below the table. The 2 kg mass moves on the table in a circle at a speed of 3.5 m/s the table top is friction less and there is no friction...

Homework Statement A block of mass m1=2kg is attached to a cord. The cord goes down through a hole in the table and is attached to mass m2=4 kg hanging below the table. The 2 kg mass moves on the table in a circle at a speed of 3.5 m/s the table top is friction less and there is no friction...

gamma is a circle of radius 2, centered at the origin, and oriented counterclockwise $\displaystyle\int_{\gamma}\frac{dz}{z^2+1} =\int_{\gamma}\frac{dz}{(z+i)(z-i)}=\frac{1}{2}\int_{\gamma}\frac{\frac{1}{z-i}}{z-(-i)}dz+\int_{\gamma}\frac{\frac{1}{z+i}}{z-i}dz = 4\pi...

The motivation: Hi, I am a bit of a space freak and I have been enthusiastic about this question for a while because there are lots of bodies in the solar system that are a few or many kilometers deep in ice. It occurred to me that if you landed your powerplant on this ice it could sink to some...

Hi all, How do I find the center of a circle given a point (tangent to the circle) and the radius. Thanks, CG

Hello! Okay so I understand that electric potential: V = kQ/r ...must be influenced by the radius doubling because it would make the potential energy half of what it originally was because of the proportionality law, v is proportional to 1/r. With electric fields though, how can...

\sum_{n=2}^{\infty}z^n\log^2(n), \ \text{where} \ z\in\mathbb{C} \sum_{n=2}^{\infty}z^n\log^2(n) = \sum_{n=0}^{\infty}z^{n+2}\log^2(n+2) By the ratio test, \lim_{n\to\infty}\left|\frac{z^{n+3}\log^2(n+3)}{z^{n+2}\log^2(n+2)}\right| \lim_{n\to\infty}\left|z\left(\frac{\log(n+3)}{ \log...

[SIZE="3"]Homework Statement Determine an expression for the Bohr radius (a_{0} from the following approximation. The electron moves to the nucleus to lower its potential energy, V(r) = -\frac{e^{2}}{r} If the electron is in domain 0\leqr\leq\bar{r}, then we may write...

I was going to post this on Earth-forum here but I thought that you guys here can help me better with this. I'm trying to get the radius of Earth on every latitude degree from 0° to 90°, knowing 0° at Equator is ~6378,137km and 90° at North/South Pole is ~6356,7523km (source Wikipedia). In...

Homework Statement By employing spherical polar coordinates show that the circumference C of a circle of radius R inscribed on a sphere S^{2} obeys the inequality C<2\piR The Attempt at a Solution I proved C=2\piR\sqrt{1-\frac{R^2}{4r^2}} So if r>R, then the equality is correct. Am I right...

Homework Statement A frustum of a right circular cone with height h, lower base radius R, and top radius r. Find it's volume. Homework Equations We are currently learning the Method of Washers and the Method of Cylindrical Shells so I believe we are supposed to use this somehow. The...

Out of many properties polymer scientists are interested to calculate one of the most common is "Rg" i.e. Radius of Gyration. Can anyone put more light on the physical significance of this value? Can Rg value of two polymers be compared? If yes what conclusion can be drawn from such comparison?

Homework Statement Estimate the radius of a spherical HII region which rests at a distance of 500 pc that subtends an angle of 20' at the observer. [1'=3x10-4 radians] Homework Equations L=D(theta) Where D is the distance, L is the angular size and theta is the angle. The Attempt...

How can I find the radius of a circle by knowing two points and its arc length? Do I have to use a numerical method to solve for a trigonometric equation or is there any algebraic or geometric method?

Hi guys, The terms above (asperity density and asperity radius of curvature) have confused me for quite a while. I've no clue what they are. Could anyone give me a hand? And is there any relation between them and the summit radius & area per summit? Thanks! CC

Homework Statement --SOLVED-- It seems, that you just apply the pythageos thereom to 'A' and 'B' =)--------------- Lets say I have a circle 'A' with radius 6cm, and a circle 'B' with radius 6cm. These two circles would have an area of 113.097cm^2. When both are combined they would have an...

Hi everyone! Nowadays, our Universe has a 47 Billions light-year long radius, but the tricky thing is that its expansion rate is increasing, so could you tell me how its radius was a couple of thousand years ago? Thanks and happy new year!

number of atoms in FCC gold cube with only the radius given! 1)it is given that the radius of a gold atom sphere is 144.2 pm, gold is packed in an FCC manner Give the ratio Ns/Nv as a function of L (gold cube side) and a parameter of FCC latice, knowing that Ns is the number of surface...

Finding the radius of convergence... Homework Statement 1+2x+(4x^(2)/2!)+(8x^(3)/3!)+(16x^(4)/4!)+(32x^(5)/5!)+... Homework Equations I would use the ratio test. Which is... lim as n→∞ (An+1/An) The Attempt at a Solution I know what to do to find the answer, but I don't know...

Homework Statement Ʃ((x-3)^(n)) / (n*2^(n)) Homework Equations lim as n→ ∞ (An+1 / An) The Attempt at a Solution When dividing two fractions, invert the second and multiple to get what you see below. (x-3)^(n+1)/((n+1)*2^(n+1)) * (n*2^(n))/((x-3)^(n)) Do some cross...

Suppose I have the Laurent series with region of convergence given below: f(z)=\sum_{n=-\infty}^{\infty} a_n z^n,\quad \sqrt{3}<|z|<\sqrt{5} Can I conclude the Laurent-Puiseux series: f(\sqrt{z})=\sum_{n=-\infty}^{\infty} a_n \left(\sqrt{z}\right)^n has a region of convergence...

Homework Statement A multi plate variable capacitor has 4 pair of plates. The plates, when closed, are separated in air by 0.01mm and a capacitance range of 10 to 400pF. a) Estimate the required radius R of each plate. b) The capacitor is set to maximum 400pF and is charged to 10V...

I've seen this thread: https://www.physicsforums.com/showthread.php?t=297842 and that is the exact question I need to to answer. What is the radius of convergence of 1/(1+x^2) expanded about x_0=1? The problem is, I can only use an argument in real analysis. I see the answer is...

Hey Guys, I having trouble with understanding radius of gyration, could someone please explain what it is? I have just never understood it's full meaning. So for example, the radius of gyration of a spinning wheel of a car is ...some value... What does that mean? Thanks

Homework Statement How much energy is required to move a 1 000-kg object from the Earth’s surface to an altitude twice the Earth’s radius? Homework Equations U = - G Me m / r The Attempt at a Solution I'm just using the above equation with 2r (twice the radius) and get 3.1 x...

Homework Statement Find the radius of convergence of sum from 1 to n of 1/(n^n) * x^(2^n) Homework Equations The Attempt at a Solution Clearly ratio test isn't going to work straight away. I'm not sure how to deal with the 2^n exponent