Radius Definition and 1000 Threads

Homework Statement The Hydroxl Ion (OH-) may be considered as a bound state of O2- and a proton. Treating the O2- ion as a nucleus of charge +8 with the electrons homogeneously distributed in a sphere of radius b, determine approximately the position of the proton, the hydroxl binding energy...

The awkward expression 1 km/s per Mpc--the radius is better It's been pointed out that by historical accident we've been stuck with an awkward mix of units conventionally used to express Hubble parameter. If you parse the quantities km/s per Mpc you find that the length units cancel and you...

How do I find the radius of the nucleus if given the mass? I am asked to compare it with the value found using the formula R= 1.2 A^(1/3)

Homework Statement A solid ball of radius rb has a uniform charge density ρ. What is the magnitude of the electric field E(r) at a distance r>r_b from the center of the ball? Homework Equations E(r) = (Q/ε)*1/Area The Attempt at a Solution If Q=ρrb and Area = (4/3)πr3...

Homework Statement Determine the radius of convergence and the interval of convergence og the folling power series: n=0 to infinity Ʃ=\frac{(2x-3)^{n}}{ln(2n+3)} Homework Equations Ratio Test The Attempt at a Solution Well I started with the ratio test but I have no clue where...

Homework Statement This problem may be dull, I know, but maybe there is a hidden math trick that i don't know of. This picture sums up the problem. So, you should prove by simplifing the integral that F^e, the eletric force applied between two spheres, onde with a charge q_1 and the...

I'm having difficulty understanding why the radius is not represented by r, but Lcostheta , isn't the entire rope in the horizontal direction? There is something I'm missing. Thanks. (Hopefully I posted this correctly.) Homework Statement The problem is example 1 on...

I am looking for some input on the proper use of the definition of the Schwarzschild radius. Case 1: In the world of black holes, the Schwarzschild radius is used in reference to the distance from the center of a mass dense enough to not allow light to exit. It is a short distance compared to...

There is this problem that I have been trying to do but I just cannot understand how to approach it. I have been doing centripetal problems for hours so maybe I am just tired. The thing is that I do not see an equation I can use to cancel out radius since the radius is not given. I have...

Homework Statement See the image below: Homework Equations In the previous part, it was proved that a particle moves through a distance x in a material without interacting with probability P given by P=\exp(-\sigma n x) Here σ represents the cross section of the reaction between...

Homework Statement (see attachment 1) In this problem, we have a row of circles placed on a line. All points of tangency are distinct. The circle ##C_n## is uniquely determined. Homework Equations The Attempt at a Solution Here's the sketch I drew for the problem. Radius...

Hi, the problem is stated as following: The Earth (mass=5.98×1024 kg) rotates around the sun in an orbit that is approximately circular, with a radius of 1.5×1011 m. Find the orbital speed of the Earth around the sun. [itеx]F=mv/r2[/itеx] I get that I need to use this equation but I'm...

Can I make a 90 degree turn on my 20 foot wide road pulling a 40 feet long and 10 feet wide cotton trailer? The cotton trailer has two axles in the rear and two axles in the front. I am an organic farmer and wish to employ a...

Hi all, Homework Statement My problem is exactly the same as the one here: https://www.physicsforums.com/showthread.php?p=2377784 In the solution that Vykan12 provides (which results in the correct answer according to the textbook), however, there is a normal force included in the...

Homework Statement you want to design a curve with a radius of curvature of 350 m, so a car can turn at a velocity of 15 m/s without relying on friction. Find the angle at which the road must be banked. Homework Equations I've derived this equation via free body diagram, x component is...

The question is: What is the minimum radius of curvature of a jet, pulling out of a vertical dive at a speed of v, if the force on the pilot's seat is 7 times his weight? The way I thought to answer this is just to say that, 7 mg, the net force on the seat will be equal to the...

The AdS4 radius is related to the cosmological constant by \Lambda =\frac{-3}{b^{2}}. Is this true in any number of dimensions, or is there a generalised relation depending on number of dimensions n?

How exactly does radius affect centripetal acceleration? In one formula we have (a=v^2/r) which implies inversely proportional, while in the other we have (a=(w^2)*r) which implies directly proportional. I understand that increasing r increases velocity (v=w*r) which means the right answer is...

We know that the escape velocity at the schwarzchild radius is c. Since the escape velocity is defined as the velocity needed to escape from the gravitational field, to reach a total energy of 0 at infinity: Doesn't this mean that an object falling from infinity starting at rest, to the...

I know the radius of a circle. I'm taking pictures of the circle as I bring it closer to the camera. Obviously the radius is getting larger. I want to know what the relationship is to find this out? I know the distance from the camera that the circle is at all times.

I didn't know whether to put this in homework or in here because it is not homework but it is a question, so sorry in advance! I like to learn about quantum physics as a hobby, and I found this great link about working with actual particle accelerator data by an organization called Quarknet...

Homework Statement Suppose c_n is the digit in the nth place of the decimal expansion of 2^1/2. Prove that the radius of convergence of \sum{c_n x^n} is equal to 1. Homework Equations The Attempt at a Solution What I want to show is that limsup |c_n|^1/n = 1. Clearly for any...

Homework Statement I need to what the escape speed from the sun to mercury would be if the spaceship is 25 mil km away from the sun. Homework Equations The Attempt at a Solution Basically, all need to know is if I can do this: Gm1m2/radius of sun+ 25 mil km away from sun=1/2 mv^2...

1. Determine the raius of convergence and interval of convergence of the power series \sum from n=1 to \infty (3+(-1)n)nxn. 2. Usually when finding the radius of convergence of a power series I start off by using the ratio test: limn\rightarrow∞|((3+(-1)n+1)n+1xn+1/ (3+(-1)n)nxn| But...

Homework Statement We have got a ball of radius r, which is falling from the roof of the house. How is the radius r with respect to time? We are looking at the ball directly from above and ball is at the beginning of fall x from our eyes. Neglect air resistance. Homework Equations I'm...

Homework Statement Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the curves about the specified axis. y=x^4, y=0, x=1; about x=2 2. The attempt at a solution I know how to do the problem, except how to find the radius. Like I know...

Dear All, I need you kind support in a problem, which I am unable to figure out. It is regarding thick lens. I am determining lens principal planes and radius using shaping factor and focal length. The forward problem I am using is, Focal length 1/f = (n-1)*[1/r1 - 1/r2...

Homework Statement Evidence for dark matter comes from “flat” rotation curves of galaxies. Assume that the observed matter moves in circular orbits about the center of the galaxy and that the velocity of the matter as a function of the radius v(r) is a constant. Also assume...

In physics class today, our teacher wanted to demonstrate that mass doesn't have an effect on fall speed. (The class was about gravitational potential energy becoming kinetic, mgh = 1/2 *mv^2 and all that) Here was the set up: He had a small rail (two parallel thin metal poles) sloping down...

Homework Statement Homework Equations Torque = Force * radius * sin(angle) The Attempt at a Solution I am trying to find the radius for the torque of the cable, but I can't seem to use any trig to solve for that side in terms of L.

Homework Statement What is the speed of the object (a bird) relative to the ground? We are given that a bird is flying in a spiraling path and rising on a thermal, making circles with a radius of 6m every 5s and rising strait up at a velocity of 3m/s.Homework Equations V=d/t C=2πr=d The...

Hi, I've come across a question that I can't seem to find an equation for anywhere, it seems to exists since I have found mention of it in various papers, but none of them listed it, or at least not in a way I could understand. The question is to find the radius of a fictional extrasolar...

Note: this is not a H.W. problem. I'm just curious about it. Imagine you are a flatlander living on a spherical planet. If you don't have any suns or any other satellites to work with how would you go about finding out what the radius of the planet is? I don't think i know enough...

Special Relativity states that a clock orbiting Earth will tick slower than one on the surface of Earth. General Relativity states the opposite - a clock will tick faster the further it is from a mass. Is there then a critical radius where these two effects cancel out? Ignore the rotation of...

Can someone shed some light on the following problem? I'm unable to get any traction on it as I know nothing about fluid dynamics (I'm a computer engineer). It's a problem I made up over a lunch discussion with a friend. I've illustrated it as folows:

Homework Statement Ʃ (from n=1 to ∞) (4x-1)^2n / (n^2) Find the radius and interval of convergenceThe Attempt at a Solution I managed to do the ratio test and get to this point: | (4x-1)^2 |< 1 But now what? How do you get the radius and interval? Any help will be appreciated! Thanks

Hi, having a bit of trouble with this question "In an argon ion laser ( λ = 514nm) the minimum beam waist is 1.0mm and is close to the plane mirror. Calculate the radius of curvature of the beam at the output mirror. 1.15m away" Attempt at a solution: θ = 2λ/pi W02 R = Z + ZR2/Z ZR =...

Homework Statement If a new planet has a year of 3.44578 Earth years, what is its radius of orbit in meters if Earth's orbital radius is 149,597,870,700 meters? Formula: r = (vt)/(2pi) How can I use this without velocity? All help is appreciated as I'm not sure how to go about this...

The rotation speed of planets around the sun follows a simple rule: if you double the distance to the sun the rotation speed is reduced by the square root of 2. No matter the mass of the planet. If Earth mass was different the period of rotation around the sun will be exactly the same. But in...

Given that the Earth has a radius of 6.4x10^6 m, what is the acceleration of a Trojan Badger launched from a catapult when it is 8.5x10^8 m above the surface of the Earth? I'm not sure how to go about this question. All help is appreciated: formulas, explanations, answers, etc.

Homework Statement Find the radius and interval of convergence for the two series: 1) [(n+1)/n]^n * (x^n), series starting at n=1. 2) ln(n)(x^n), series starting at n=1. Homework Equations You're usually supposed to root or ratio your way through these. The Attempt at a...

1. Calculate the schwarzschild radius of a proton 2. R = (2MG)/c^2 3. I plugged in m= 1.67E-27, G=6.67E-11 and c=3E-8 and got out an answer of 2.5E-54. This seems ridiculously small, but I can't figure our if I'm doing something wrong or if it really is just that tiny. The next...

Hi All, I'm not a math guy so I am coming to you for help. I am trying to come up with an equation to graph any 180 degree curve that is comprised of: a 135 degree radius, and a 45 degree ellipse (135 + 45 = 180). The two curves being the same curvature (slope?) where they meet. The portion...

Homework Statement I asked a similar question before relating to an animal's foraging radius. I think there was a typo but I'd like to show another example to see if I'm on the right track. The parameter values are as follows: Q= 5.2 × 106 J C = 1.5kg d= 0.055kg per hour k= 2.0...

ƩHomework Statement Determine the radius of convergence and the interval of convergence for the follwing function expanded about the point a=2. f(x)= ln(3-x) Homework Equations ln(1-x) = Ʃ (x^n+1)/n+1 n=0 which has radius of convergence at |x|<1 The Attempt at a Solution...

I am under the impression that the event horizon radius of a non-rotating black hole is equal to its Schwarzschild radius. Is this correct? If yes, then I have a mixed bag of questions: Is the event horizon radius always calculated using the Schwarzschild metric, no matter what model we are...

Homework Statement A 0.125kg basketball is rolling w/out slipping on a horizontal table at 4.50 m/s when it rolls off the edge and it falls to the floor, 1.10 m below. What is the rotational kinetic energy of the ball right before hitting floor?Homework Equations KE rot: .5 I w^2 KE...

Homework Statement The nuclei ^{41}_{21}Sc and ^{41}_{20}Ca are said to be a pair of mirror nuclei. If the binding energy of ^{41}_{21}Sc and ^{41}_{20}Ca is 343.143 MeV and 350.420 MeV, respectively, estimate the radii of the two nuclei with the aid of the Semi-Empirical Mass Formula...

Homework Statement A manufacturer of CD-ROM drives claims that the player can spin the disc as frequently as 1200 revolutions per minute. a. If spinning at this rate, what is the speed of the outer row of data on the disc; this row is located 5.6 cm from the center of the disc? b. What is the...

If the mass of the planet is 1.38 x 10^25 kg and its radius is 4.30 x 10^7 m... Homework Statement {attachment} (all the formulas in the attachment too) I don't know how to start this question Please help -[