Radius Definition and 1000 Threads

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

A cylindrical can with height h and radius r is to be used to store vegetarian chilli. It is to be made with 6 square centimetres of tin. Find the height h and radius r which maximizes the volume of the can. Hint: The volume of a cylinder is r2h and the surface area of the side walls of a...

Hello everybody, I'm not sure if this post is more appropriate here or in the physics section (it's about biophysics topics): if it's off-topic here, please excuse me and move it. I was wondering if it's possible to calculate the enthalpy of formation of a gas molecule, in this example...

Homework Statement A roll of toilet paper ( a partially hollow cylinder with R2=7.0 cm, M=320 g, I=6.0x 10 ^(-4) kg m is mounted on an axle. initially at rest, until a child grabs the end and starts running at a constant linear acceleration. part a) what is the inner radius (R1)Homework...

Homework Statement The International Space Station (ISS) circles the Earth at an altitude of 347 km. What is the period of the orbit of the ISS expressed in minutes? G=6.67x10^-11 N * m^2 /kg^2 M(Earth)=5.98*10^24 kg Homework Equations T^2/R^3 = (4Pi^2)/(GM) So: T^2=...

Homework Statement The rollercoaster moves freely without negligible friction. The radius of the loop is 20m and the car barely makes it through the loop. Find the speed at position 3. Find the speed at position 1 and 2. Find the difference in height between position 1 and 4 if the speed...

Homework Statement Calculate the centripetal acceleration module in the following cases as a multiple of g = 9.8 m / s ^ 2. a) a car traveling at 100km / h on a curve of radius 50m. b) a jet plane flying at 1,500 km / h and making a turning radius of 5km. c) a stone that is rotated every...

Homework Statement The Attempt at a Solution So my first thought is that the only way to solve this problem is to apply a characterization of a cyclic quadrilateral. We know that the perpendicular bisectors of a cyclic quadrilateral are concurrent. So here's my thoughts: Construct...

Homework Statement Calculate the electron concentrations (# electrons/atom) needed for the fermi sphere to contact the zone faces (first bril. zone edges) in BCC and FCC structures. Homework Equations kf = (3*pi^2*n)^(1/3) where n is # electrons per atom. For cubic structures...

Hi, there. I have a question： If I want to build a facility for synchrotron RADIATION (not for particle physics experiment), how to chose the radius of the storage ring? (Why the radii of current facilities are so large?) Thank you.

When I use the calculation from Wikipedia that says that the radius of convergence of a series is lim as n goes to infinity of |an/an+1|, I get for the Taylor series expansion of ln(x) around a=2 the answer of an infinite radius of convergence, which would mean that it would be valid everywhere...

Homework Statement We are asked to calculate the flux at a specific wavelength (f_5500), the surface flux(F) and the radius of a star (Sirius A and then B) We are given the following: Brightness of Sirius A: V=-1.47 Effective temperature: 9870K Central wavelength: 5510 Angstroms Filter...

Homework Statement i was doing this exercise and came across this example. ∞ Ʃ (x^n)/ln(n+1) n=1 The Attempt at a Solution i know you have to do the ratio test which is lim | a(n+1)/a(n)| n>∞ i got to lim | [x ln(n+1)] /ln(n+2) | n>∞ and have no idea how to continue? is...

Homework Statement Hi there, I have just started taylor series for my course.. most seems arlgiht so far, however when it comes to validating a given series( tayor or maclaruin), I have an idea on how to find out the x value.. but I don't know what I am doing wrong.Take for example: The...

Homework Statement Hello everybody, I have a question that is tied into my lab report regarding centripetal force. The question asks if the frequency of rotation were to increase how would the radius r and the centripetal force change? Homework Equations 2\pif = v/r rearrange for...

With <Rg^2>=1/N [sum[(Ri-Rc)^{2}>] where Rc is the center of mass, =1/N sum Ri, and provided that <R^2>=2Lζ .Show that sqrt(R^{2})=sqrt(L ζ /3)

Homework Statement A box with mass 2kg is on the edge of a circular platform of radius 6.0m. The coefficient of friction between the platform and the box is 0.3. The platform accelerates. Determine the speed when the box slips off the edge.Homework Equations Fs = μsN F⃗ net=ΣF⃗ =ma⃗ a(t) =...

Homework Statement Parallel light in air enters a transparent medium of refractive index 1.33 and is focused 35 mm behind the surface. Calculate the radius of curvature of the surface of the medium Homework Equations f = \frac{R}{2} \frac{1}{f}=(n-1) \left(...

Homework Statement Suppose that Captain Omega of the Imperial Space Patrol wishes to place a spy satellite in geosynchronous orbit above the mysterious Planet X, which has a mass of 5.90 x1024 kg, and a rotational period of 26.4 hours. (a) What should be the radius of the satellite's orbit...

Homework Statement The Earth is 6371km in diameter and this is equivalent to 1 mass. If I increase the Earth's mass to 2x what will be its diameter? What is the formula to compute this?Homework Equations The Attempt at a Solution PS: This is my first post and I wish to say hello to everyone!

Homework Statement Okay, the assignment involves electron beams of various voltages, currents, and radii Basically, the situation is, several of these beams were measured for the aforesaid values. The values as follow are in the following order - Voltage (J/c) - Current in Helmholtz Coils (A) -...

I researched this some, but could not find a method to calculate the radius of the ring singularity in a Kerr black hole. I would think it is a function only of black hole mass and angular velocity. Please let me know if there is some reports or papers on this.

Homework Statement A uniform magnetic field of magnitude 0.137 T is directed along the positive x axis. A positron moving at a speed of 5.40 106 m/s enters the field along a direction that makes an angle of θ = 85.0° with the x-axis (see figure below). The motion of the particle is expected...

Homework Statement 1. An oil tanker springs a leak creating a circular oil slick that grows until its radius is 3.0 km. a.) What is the formula describing the relation between the area of the slick and its radius? Homework Equations Area of a circle: (pi)r^2 The Attempt at a...

Homework Statement How much acoustic power propagates through a spherical surface (sound source in centre) with radius equal to 1.0m? with radius equal to 5.0m? I = 10^-2 W/m^2 r = 1.0m or 5.0m f = 50kHz t = 2.0*10^-3s IL = 100dB Homework Equations I = P/4∏r^2 The Attempt at a...

Homework Statement In Millikan's experiment, an oil drop of radius 1.73 μm and density 0.865 g/cm3 is suspended in chamber C when a downward electric field of 1.44 × 105 N/C is applied. Find the charge on the drop, in terms of e. (Tolerance of solution is +/- 2%) Known: radius, r = 1.73...

Okay this seems like a really simple question. Basically I'm adding together 8 spheres (like raindrops coalescing into one bigger drop) and I'm getting two different answers for the new radius. Each individual drop is identical. I start by expressing the new volume in terms of the...

Homework Statement An Earth satellite moves in a circular orbit with an orbital speed of 6200 m/s. Find the time of one rotation as well as the radial acceleration of the satellite in orbit. Homework Equations Ac= V^2/R mAc=mg V= 2(pi)R/t The Attempt at a Solution Ok, I've...

Homework Statement Show that for every a* = (a1, 1/a1), there exists another point of the form (a, 1/a) in a ball (i.e. circle, since we're in R2) of radius r, centered at a*, for any r > 0. The Attempt at a Solution This is actually only a part of the whole problem, but I just can't put it...

Homework Statement 1)Determine the radius of the allowed orbits. Calculate the first orbit of Bohr's model for the hydrogen atom. 2)Show that the energy is quantized. Calculate the energy of an electron on the first orbit (fundamental state of hydrogen atom)Homework Equations L=n \hbar...

(a) Find the surface area, S, as a function of r. S = 2*pi*r^2 + 2*pi*r*h I know how the 2pi(r)^2 is found, but where does the 2*pi*r*h come from? (b) What happens to the value of S as r goes to infinity? S also goes to infinity. As r increases, S increases. (c) Sketch a graph of...

Centripetal Acceleration with infinite Radius?? Homework Statement Find centripetal acceleration given speed is 38m/s and radius is infinity large The Attempt at a Solution So The answer would get infinitely smaller so is zero the best answer?

Homework Statement A civil engineer is asked to design a curved section of roadway that meets the following conditions: With ice on the road, when the coefficient of static friction between the road and rubber is 0.1, a car at rest must not slide into the ditch and a car traveling less than 80...

Homework Statement I've already answered the first part. The second part is what's giving me trouble. Homework Equations Here's how I solved #10: Since the car is at rest, we're only worried about the force of friction and the parallel component of gravity: F_f = F_g *...

Homework Statement 15MeV electrons, enter magnetic field with strength of 0.7T. What is the radius of the path of the electrons? What energies could the electrons have and be confined to orbits with radii within 5% of the 15MeV electrons? Homework Equations E =...

Homework Statement Calculate the radius of the Earth's core using the following data: Pe = 5,515 kg/m^3 (earth's average density) Pc = 11,000 kg/m^3 (core's density) Pm = 4,450 kg/m^3 (mantle-crust density) Re = 6377km (radius of the earth) Homework Equations im guessing we...

Homework Statement Ok here is the question, and I will give the answer below. I am not really clear on how the instructor got this answer. So, if anyone could explain the answer a little, I would REALLY appreciate it! Question: A spherical balloon with radius r centimeters has volume...

Homework Statement 20 lbs. on the end of a 30 inch arm. Dropping from 2oclock position to 5oclock position. How much wieght will be developed if this was dropped on a scale measuring lbs. Homework Equations I am unsure how to calculate this. The Attempt at a Solution If there is...

Homework Statement For f(z) = 1/(1+z^2) a) find the taylor series centred at the origin and the radius of convergence. b)find the laurent series for the annulus centred at the origin with inner radius given by the r.o.c. from part a), and an arbitrarily large outer radius. Homework...

I need find the thickness of a piece of paper based on the known linear speed of the paper coming off the roll and the change in diameter of the roll. I have the ability to see the linear speed. It is consistant but changes from roll to roll. I know the starting radius, instantaneous radius...