Radius Definition and 1000 Threads

How far down can a nickel ball of radius r and temperature Tn melt into the ice block of temperature Ti? Watch the video and state your assumtpions...

Homework Statement A particle is moving on a path parameterized as such: $$x(t)=a\sinωt \quad y(t)=b\cosωt$$ Find the radius of curvature ρ as a function of time. Give your answer in Cartesian coordinates. Homework Equations $$\frac{1} {Radius~of~curvature}=|\frac{de_t}{ds}| $$, where et is...

Homework Statement A car traveling 10 m/s is moving along a track banked at 5 degrees. The tire-road friction coefficient is .3 What is the minimum radius it can travel without slipping? v0= 10 m/s Bank Angle Θ = 5° μ=0.3 Note I am working through prep material for the exam. The solution...

I am trying to predict the radius of a bubble at 0.4 m deep in a liquid. I know: the surface tension of the liquid (T) .002239 kg*m the pressure outside the bubble at .5 meters depth (Po1) 394.5 kg/m^2 the pressure inside the bubble at .5 meters depth (PI1) 394.723314 kg/m^2 the radius of the...

I am interested to find the length shown in red in the attached figure. I want this length as a function of d (shown in blue) and the angle θ. Then I will integrate this length to dθ from 0 to π/2. Firstly, I used the law of the triangle to determine the length s which when subtracted from the...

Homework Statement This is the main question.So I'm stuck at the b part It says that the shell radius is (3)^1/2 - (3-y^2)^1/2 but i would only say (3-y^2)^1/2.Why do we say otherwise? Homework EquationsThe Attempt at a Solution i would say the shell radius is (3-y^2)^1/2 but it's wrong

Is there theoretically a smallest possible Schwarzschild radius?

Suppose that there's a wheel. A constant torque is applied to the wheel from the central axis. What is the relationship between the amount of force received by each particle on the wheel in relation to the distance each particle is away from the axis?

Homework Statement Σ(n=0 to ∞) ((20)(-1)^n(x^(3n))/8^(n+1) Homework Equations Ratio test for Power Series: ρ=lim(n->∞) a_(n+1)/a_n The Attempt at a Solution I tried the ratio test for Power Series and it went like this: ρ=lim(n->∞) (|x|^(3n+1)*8^(n+1))/(|x|^(3n)*8^(n+2)) =20|x|/8 lim(n->∞)...

Hi, I'm trying to understand how Differentiation and integral works in practice, and would really appreciate some help interpreting this calculation- If we have a circle with Area A=pi*r^2 1) If i want to find the change in Area with respect to radius then dA/dr= 2pi*r2) If I'm told...

Homework Statement If the coefficient of static friction is 0.38 (wet pavement), at what range of speeds can a car safely make the curve? [Hint: Consider the direction of the friction force when the car goes too slow or too fast.] Homework Equations I am trying to figure out the Vmax 3. The...

Hi everyone, I am trying to evaluate the radius of convergence for the following power series: (k!(x-1)k)/((2k)(kk)) I have begun by trying to compute L = lim k-->inf (an+1/an). To then be able to say R = 1/L. So far i have L = lim k--> inf (kk(k+1)!)/(2(k+1)k+1k!) From here i am having...

I am attempting to evaluate the radius of convergence for a series that goes from k=0 to infinity. The series is given by (k*x^k)/(3^k). I have begun by using the ratio test and have gotten to the point L = (k+1)*x/3k Now i know i can find out the radius of convergence by simply saying R =...

Homework Statement so my friend asked this question: "what's the atomic radius ratio between He-3 and He-4?" 2. Homework Equations all i know is this equation : r =nh/mv 3. The Attempt at a Solution i thought the ratio will be same because both He-3 and He-4 have only two electrons. Correct...

Hello! (Wave) $$e^x= \sum_{n=0}^{\infty} \frac{x^n}{n!} \forall x \in \mathbb{R}$$ i.e. the radius of convergence of $\sum_{n=0}^{\infty} \frac{x^n}{n!}$ is $+\infty$. Could you explain me how we deduce that the radius of convergence of $\sum_{n=0}^{\infty} \frac{x^n}{n!}$ is $+\infty$? Do...

Just double checking this - I found this formula describing the radius of the path of an ion in a cyclotron: R = sqrt(2*E*m)/(e*B) .. where R is the radius in meters, E is the energy of the particle in joules, m is the mass in kilograms, c is the charge in coulombs, and B is the strength of...

Hello Physics Peeps, It just came up in the notes for my electrodynamics class that an electrons charge squared can be expressed as the radius times the mass times the speed of light squared. e^2 = m_er_ec^2 I don't understand the motivation for doing this. I've tried to search for other...

We know that universe is expanding .I am curious about how universe radius change with time or simply R(t)=? (Observable universe radius)

Homework Statement A muon is a particle with a charge equal to that of an electron and a mass equal to 207 times the mass of an electron. What is the radius and energy of the ground state of hydrogen if the electron is replaced with a muon? Don't forget to use the concept of reduced mass...

What is the meaning of r in the Schwartzschild metric?. ds^2 = \frac{{dr^2 }}{{1 - \frac{{2GM}}{{c^2 r}}}} + r^2 (d\theta ^2 + \sin ^2 \theta d\varphi ^2 ) - c^2 \left( {1 - \frac{{2GM}}{{c^2 r}}} \right)dt^2 If you were to actually measure the radius, your observation would be affected by...

Hi, Assuming the electron is a sphere of finite extent, the classical electron radius is derived by equating the energy of the electric field with mec2. For the computation of the field energy, we have to assume a charge distribution. Both constant charge density and constant surface density...

Homework Statement The planet Saturn will orbit the Sun every 19 Earth years (= 599 184 000 seconds). Assume Saturn travels on a circular orbit with a speed of 9 690m/s. What is the radius of the orbit of Saturn? I can solve this in two different ways, and get two different values. Which is...

A 2013 paper ( http://arxiv.org/pdf/1312.4854v1.pdf ) gives the following: Ωk = 0.0010 ± 0.0029. Can a value for the radius of curvature be determined from Ωk = 0.0010? If so, what is it, and what is the formula? If not, why not?

I have great trouble with the concept of 'local' as it seems very generic in ways. Local can be a plank distance away, or a meter away.. or even a Hubble radius away (if your scale is in Hubble radii (sp) or so). If distance in the direction of travel approaches zero as velocity approaches the...

Hi guys, was wondering if anyone could help me solve this problem. Thanks!

Hello friends, I am working on a design project for my capstone course in my engineering curriculum. Part of the design involves a cord consisting of wires tightly wrapped helically (à la a spring) around a nylon rope core. An important specification of this design is the radius of curvature...

Do you guys know of any program that can give me the radius of a circumference, if I input the cartesian coordinates of some points?

Homework Statement Consider a satellite in circular low Mars orbit 300km above the planetary surface. R = 3396km M = 6.419 x 1023kg G = 6.674 x 10-11m3/kg/s2 Find the orbital velocity of the satellite (using the given values, I assume, as there is some inaccuracy in the real-life mass value...

Hello ! I would like to know if the following relation, which numerically holds true according to the data available on wikipedia, can be analytically deduced from the current standard physics and model of a proton: R = 4 x L x ( M / m ) =4 x 1.61619997e−35 x 2.1765113e−8 / 1.67262177774e−27 =...

Proving elipsoide radius of axis i equals 1/sqrt(λi) How is radius related to eigenvalues? I can't find the connection ... :S

Homework Statement A geostationary satellite is to be placed to view the far side of the moon. How far away should it be placed from the center of the Earth and what velocity should it travel in order to maintain its orbit? (Considering the moon and Earth as one entity and solve for the center...

Homework Statement A small solid sphere of mass M0, of radius R0, and of uniform density ρ0 is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls...

Hi, I am a first time poster and I am completely lost with this question. Any help would be greatly appreciated Filling the space between a contact lens and the cornea is a small quantity of liquid of refractive index of 1.336. Assuming the refractive index of the lens material is 1.490 find...

Hi, I am a first time poster and I am completely lost with this question. Any help would be greatly appreciated Filling the space between a contact lens and the cornea is a small quantity of liquid of refractive index of 1.336. Assuming the refractive index of the lens material is 1.490 find...

Homework Statement A thin circular ring of radius R has charge Q/2 uniformly distributed on the top half, and -Q/2 on the bottom half. a) What is the value of the electric potential at a point a distance x along the axis through the center of the circle? b) What can you say about the electric...

Hi, I'm trying to make a simple model of stellar evolution for a game project of mine, but I'm not sure how to predict the radius of a star's core without reference to its surface radius. I am trying to derive the surface radius from the amount of energy being released by the core. The goal is...

Homework Statement What is the largest possible radius of a sphere which is inscribed in a regular tetrahedron a=10 ( this is the side of the tetrahedron) r=? r=5*√6/6 Homework EquationsThe Attempt at a Solution So first I calculated the Height of pyramid a2=(2/3*va)2+h2 h=√(a2-(2/3*a*√3/2)2)...

Is it possible to derive r=GM/c^2 classically(as in Newtonian gravity) without using eeinstein field equation?

I was sitting down thinking yesterday, I know that it was worked out through the ages by various methods. But how did we come to the value which we have today? All I can seem to find on the subject is this https://heasarc.gsfc.nasa.gov/docs/cosmic/earth_info.html which says that it is determined...

Homework Statement I'm doing a coursework where I must find the angular acceleration of a rolling tin can using theoretical values. I have its mass and radius. I actually have experimental data so i have access to the actual values of angular velocity and angular acceleration, as well as time...

Homework Statement How do you calculate the mass of an object just from the acceleration from gravity and the radius? Homework Equations My thoughts were F=GM/r2, then once you find F, you can calculate mass by M=F/A G= 6.67 x 10^11 r = 12 Acceleration = 2 m/s^2 The Attempt at a Solution...

This was a homework problem; after five tries, I still did not get it, and I can't figure out how to get at the answer the assignment gave me. I could not find the answer anywhere that didn't get into angular velocity, which we are not at yet (and also did not give me the answer!). 1. Problem...

Homework Statement Find the potential V(r) inside and outside of a uniformly charged sphere with radius R and total charge q. A) Fix first the charge density ρ(r) in the two regions 1: r>R and 2: 0<r<R the results should only be in terms of q and R[/B] Homework Equations ρ= qtot/Vtot dq=...

Homework Statement A circular space hotel in orbit around the Earth has a radius of 220m. in order to produce "fake gravity" along the outer rim, it is desired to rotate at a speed that will produce a centripetal acceleration of 9.81 m/s^2. A) find the tangential speed of appoint on the rim...

Hi there, I was reading one of my textbooks and I had a thought. For a black hole, there is minimum orbiting radius of ##R_{min}=3R_s## where ##R_s## is the Schwarzschild Radius. This minimum orbit is created by the fact that in order to obtain an orbit of that radius around a black hole, you...

Homework Statement z ∈ ℂ What is the radius of convergence of (n=0 to ∞) Σ anzn? Homework Equations I used the Cauchy-Hardamard Theorem and found the lim sup of the convergent subsequences. a_n = \frac{n+(-1)^n}{n^2} limn→∞ |an|1/n The Attempt at a Solution I think that the radius of...

About: As a project, I'm trying to solve for the approximate radius and mass of a approximately earth-sized planet, Mann, from Interstellar. According to what was provided, g = 7.84m/s2 The solid part of the planet is composed of a honeycomb of rock and ice The space inside the honeycomb is...

I'm a beginner in GR (as you may conclude from some of my previous posts) so any help is greatly appreciated. I was recently studying alternative metrics for the Schwarzschild metric and one of them was the Kruskal Szekeres metric. In Schwarzschild, the radius r is defined which is the radius...

which formula is correct? or

Hi, I'm trying to solve the following problem: "What is the optical power (in dioptres) of a concave-convex eyeglass lens (n = 1.5) with the radiuses r1 = 12cm and r2 = 18cm?" The attempt at a solution: I'm usually solving such questions with the following equation: ## \dfrac{1}{f} =...