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  1. K

    Hilbert's Grand Hotel Paradox

    Homework Statement Suppose that Hilbert's Grand HOtel is fully occupied on the day that the hotel closes all the even numbered rooms for maintenance. Show that all guests can remain at the hotel Homework Equations The Attempt at a Solution I am not quite sure how to solve this, my...
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    Pendulum moving with constant veloctiy

    Homework Statement Consider a pendulum that consists of a mass M hanging from a massless string of length r. The string is being pulled upward at constant velocity through a tiny hole in the ceiling, so the length of the pendulum is given by r = r0 - alpha*t, where alpha is a constant. Let...
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    Darwin and relativistic kinetic energy correction for hydrogen

    Homework Statement Combine the Darwin correction with the relativistic kinetic energy correction for l=0 to show that the fine structure formula: \DeltaE_{fs}= - \frac{(E^{(0)2}_{n})}{2mc^{2}}[\frac{4n}{j + 1/2}-3] remains valid for l=0 Homework Equations From a previous problem...
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    Undergraduate CV

    I am currently composing a CV for research positions and I have only a minimal amount research experience and I am trying to beef up my CV, and I was looking for suggestions as to what to include and what not to include. Thanks
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    Work expended moving a charge

    Homework Statement q3---a-----| | | | b | | q1---------q2 The figure shows three charges q1, q2 and q3 situated at corners of a rectangle of sides a = 15.0 cm and b = 6.0 cm. For q1 = 5.90 μC, q2 = -5.90 μC, and q3 = 1.60 μC find the electric...
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    Relative error definition of entropy

    Homework Statement Problem-5: In the class we saw that property of additivity of the entropy for systems in thermalcontact relies on the approximation that we compute entropy of the most probable state ln(g1g2)maxinstead of full ln g(N,U) = ln(P,U1) g(N1,U1)g(N2,U −U1)). The error made turns...
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    Electric force on a charge

    Homework Statement Q1-----Q2-----Q3; Q1=1.78E-6C;Q2=Q3=-Q1, r1=r2=1.82m Calculate the total force on Q2. Give your answer with a positive number for a force directed to the right. Homework Equations F= kq1q2/r^2 The Attempt at a Solution F2 = F12+F23 F12 =...
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    Positive oscillatory solution

    Homework Statement For the oscillatory solution (+k2) solution, suppose x is restricted to 0\leqx\leqa by requiring \psi(x)=0 and \psi(a)=0, what are the restrictions on A,B and k? Homework Equations given \psi(x)=Acos(kx)+Bsin(kx) The Attempt at a Solution so, I pretty just...
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    Yield of nuclear bomb

    Homework Statement The energy released by nuclear bombs is measured in kiloton (kt) or megaton (Mt) units. One kiloton is a unit of energy released by 1000 tons of trinitrotoluene (TNT). One kiloton is 4.2×1012 joules. The yield of fission bombs is typically between 10 and 500 kilotons, the...
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    Mass of Fuel Rods

    Homework Statement The electric power generated by a single average size nuclear reactor block is between 400 and 800 MW. The fission of one 235U nucleus generates 185 MeV energy on average. What is the total mass of the fuel rods loaded into a 760 MW reactor for a one year period, if the...
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    Weizacker Formula Equation

    Homework Statement For 58Ni: B(AZX) = aVA - aAA^2/3 - aC[Z(Z-1)]A^-1/3 - aS[(N-Z)^2]/A + δ. Using the parameter values given by Enrico Fermi (aV = 14 MeV, aA = 13 MeV, aC = 0.72 MeV, aS = 19 MeV, ∆ = 33 MeV · A-3/4), determine each term in the formula. Calculate the magnitude of the...
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    Mathematica Plotting arbitrary constants in mathematica

    How do you plot arbitrary constants in mathematica? for example r(psi)=a(1-eCos(psi)), where a and e are some constant. Thanks in advance for the help.
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    Anomalous zeeman effect

    Homework Statement The anomalous Zeeman effect is studied in an advanced student laboratory. A spectral lamp is filled with the vapor of an unknown atom. (It is unknown to the student.) The atoms are excited to the 2D5/2 state with a high frequency electromagnetic field. When a static magnetic...
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    Minimum velocity to change radius of orbit

    Homework Statement A rocket is in an elliptical orbit around the earth; the radius varies between 1.12 Rearth and 1.24 Rearth. To put the rocket into an escape orbit, its engine is fired briefly in the direction tangent to the orbit when the rocket is at perigee, changing the rocket's velocity...
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    Roller coaster speed problem

    Homework Statement A roller coaster is at the top of a slope moving very slowly. There are three lengths in this problem: h = 53 m is the height of the hill; D = 65 m is the length of the hill; L = 43 m is the length of the coaster. Derive an equation for the speed v1 when the first car...
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    Projectile fired from earth

    Homework Statement A projectile of mass m is fired from the surface of the earth at an angle α from the vertical, where α = 0.34 radians. The initial speed v0 is equal to √{GM/Rearth}. Calculate the maximum height that the projectile will reach. Neglect air resistance and the earth's...
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    Normal Zeeman effect of hydrogen atoms

    Homework Statement When specially prepared Hydrogen atoms with their electrons in the 6d state are placed into a strong uniform magnetic field, the degenerate energy levels split into several levels. This is the so called normal Zeeman effect. A) Ignoring the electron spin what is the...
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    Pumped energy storage

    Homework Statement Pumped Energy Storage. A water reservoir has surface area A and depth D. The water flows down pipes and through turbines to generate electric power. The bottom of the reservoir is at height H above the turbines. The depth D of water in the reservoir decreases at a rate δ...
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    Force on a massive ring

    Homework Statement A massive ring (radius = a and mass = M) lies on the xy plane. Calculate the force F on a test mass m at position z on the z axis. Now assume a = 1 and GMm/a2 = 1 in some system of units. (a) What is the force on m at z = 0? I got the answer for this its 0 (b) What...
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    Frictional force by tires

    [Homework Statement An SUV pulls a trailer carrying a boat. The mass of the SUV is 2460 kg and the mass of the boat and trailer is 490 kg. The SUV starts from rest (velocity = 0) and accelerates for 10 seconds to final velocity 12 m/s; i.e., a = 1.2 m/s2. What is the frictional force...
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    Undetermined coeff. solution

    Homework Statement I am stuck on this and just need to know the form of the solution for undetermined coeffecients of y''+y'+y=(1-e^-t) my guess is A-Ae^-t but im not sure
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    Programs Advice for a minor

    I am currently going into my sophomore year at a university majoring in physics, and looking to gain a minor in something useful(either math or cs). Which would be more beneficial, I would think cs. Also, I want to learn a foreign language, but which would be best, as of now I am thnking either...
  23. K

    Radius of Earth's Iron Core

    Homework Statement Consider a simple model for the interior of the Earth: there is a spherical iron core with constant mass density ρ0 and radius a; outside the core is "rock" with constant density ρ1. Use these values for the densities: ρ0= 8.90×103 kg/m3 and ρ1= 3.80×103 kg/m3. The radius...
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    Job Skills Resume advice for undergrad

    Hi, I am currently going into my sophomore year majoring in physics. I am trying to get a job or volunteer position to gain some research experience and I am trying to make a resume, however, seeing as how I have no prior research experience, I was wondering what I should put on it. Thanks
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    Aplha particle tunneling through coloumb barrier

    Homework Statement Let us approximate the Coulomb barrier of a heavy nucleus by a square potential with a height of V0 = 14.8 MeV and a width of L = 13.7 fm. What is the probability that an α particle with an energy of 5.70 MeV will tunnel through this barrier? Homework Equations...
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    Relative energies inside a rectangular box

    Homework Statement Consider a three dimensional rectangular infinite potential well with sides of length L, 2L and 3L. What is the energy of the first excited state relative to the energy of the ground state? The second state? The third? The fourth? Homework Equations...
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    Critically damped oscillations

    Homework Statement A mass m moves in one dimension x subject to a restoring force −kx and a damping force −γ[(x)\dot]. What are the conditions for underdamped oscillations, overdamped oscillations, and critical damping? Now, suppose m is 0.80 kg, γ is 1.18 kg/s, and the oscillations are...
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    Cuckoo clock pendulum

    Homework Statement Consider a small cuckoo clock in which the length of the pendulum is L, suspending a mass m with a period of oscillation T. The clock is powered by a falling weight (mass = M) which falls 2 m between the daily windings. The amplitude of the swing is 0.2 radians. (A)...
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    Probability inside finite square well

    Homework Statement What is the probability, that the particle is in the first third of the well, when it is in the ground state? Homework Equations \Psi(x)=Asin((n*pi)/L) A=(2/L)1/2 The Attempt at a Solution so probablility is related to the wave function by \Psi2 so i...
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    Finding wavelength of an electron

    Homework Statement What is the wavelength of an electron with a kinetic energy of 2.00 MeV? What is the wavelength of an electron with a kinetic energy of 2.08 GeV? (Possibly useful constants: hc = 1239.8 eVnm, rest energy of the electron: E0,e = 511.0 keV.) Homework Equations...