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    Intensity of natural light after polarization

    I read that if a beam of unpolarized light goes through a polarizer, the intensity of the polarized beam is equal to half the intensity of the original beam. Can someone explain me why? I thought the intensity would be the same.
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    Theory of small oscilations

    Homework Statement (see pic) \frac{l_{2}}{l_{1}} = \frac{1}{4} \frac{g}{l_{1}} = 1 I need to find the normal modes of oscillation. (for small oscillations) The Attempt at a Solution I solved the problem using the matricial way and got the following matrix: (I simplified it using the...
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    Classical mechanics

    Ayo everybody, I'm doing a problem about theory of small oscilatons (see pic) and I got the following for potential energy: V= mg(\frac{l_{2}}{2} +\frac{l_{1}}{2} \theta^{2}_{1} + \frac{l_{2}}{4} \theta^{2}_{2}) (after the aproximation cos \theta ~ 1 - \frac{\theta^{2}}{2} Knowing that V...
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    Determine the wave function of the particle

    Homework Statement A particle coming from +∞ with energy E colides with a potential of the form: V = ∞ , x<0 (III) V = -V0 , 0<x<a (II) V = 0, x>a (I) a) Determine the wave function of the particle considering that the amplitude of the incident wave is A. Writting the amplitude of the...
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    Infinite potential

    Potential and wave function If a particle comes from +infinite and collides with a potential of the form : V = ∞ , x < 0 (I) -V0 , 0<x<a (II) 0 , x≥a (III) Is the wave function for region (I) = 0? And for region (II) = A sin(kx) with k constant? Really need to...
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    Cosmic simulation software

    Hey, does anyone know what software is used on the astrophysics videos made by NASA? Or similar modeling software where I can play around a bit creating solar systems and stuff like that? Thanks
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    Bar suspended by rope kinetic energy

    If I needed to calculate the kinetic energy of a bar suspended by a rope at one of its ends, in other words, a bar pendulum, do I need to calculate the kinetic energy of the center of mass plus the kinetic energy relatively to the center of mass or do I need to calculate the kinetic energy of...
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    Linearly changing density

    Homework Statement I need to find the Kinetic energy of a bar rotating about its center of mass. I know the bar as length 3b and it's center of mass is located at 2b, the bar density changes linearly along it's length. Homework Equations T=1/2 W^2 I The Attempt at a Solution...
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    Potential well

    Homework Statement At the instant t=0, there's a system with 1000 particles in a box of length a. It is known that 100 have energy 4E1 and 900 have energy 225E1, where E1 is the energy of the fundamental state. i) Build a wave function that can represent the state of a particle ii) How many...
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    Angular moment cube

    Homework Statement An homogeneous cube of mass M and side 2a spins around one diagonal of the faces with constant angular velocity w. Show that the size of the angular moment in relation to one of the fixed vertexes is \sqrt{\frac{43}{3}}Ma^2w What I visualize here is a cube with one of its...
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    Hoop kinetic energy

    Hey PF, this is just a quick question: If there's a hoop of mass M and radius a rotating around its vertical axis (see pic) and I want to write the kinetic energy for the Lagrangian is it just T = \frac{1}{2} M a^2 w^2 ? Considering w the angular velocity
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    Capacitor AC

    Homework Statement consider a capacitor with circular plates of radius a, separated by a distance d (d<<a) and V(t)=V_{0}sin(wt) a)Considering the z axis to be the capacitor axis, verify that the electric field between the plates is , in good approximation, given by \vec{E}(t)\approx E_{0}...
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    Potential energy of spring and mass system

    Homework Statement O^^^^^^O^^^^^^O |------------------------------------------→ There are 3 equal masses connected by springs with lenght a and spring constant k. The system can only move in the x axis. x1,x2,x3 is the position of each mass What is...
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    Lagrange mechanics

    Homework Statement A particle of mass m moves over the cylindrical surface of radius R. The particle is connected to the origin O, located on the central point of the cylindrical surface axis, by a spring with spring constant k and lenght R. Ignore force of gravity. a) State how many...
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    Classical mechanics: orbits, force, potential

    Homework Statement a particle of mass m moves on the orbit r= a cos(θ), a>0. Find the force acting on the particle The Attempt at a Solution I had this formula in my notebook: U(r)= E-(L^2/2mr^2)(1+(1/r^2)(dr/dθ)^2) Using it I got U(r)=E-L^2a^2/2mr^4 and F(r)=-dU/dr=...
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    Electric fields and a spherical surface

    If there's a point charge Q at the center of a spherical surface(of radius a) made of conducting material that is connected to earth, why is the electric field past r>a zero ? Doesn't it imply that the spherical surface becomes charged with -Q ? And why is that? What would be the...
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    Eletric potential inside charged sphere with hole inside

    Homework Statement Consider a charge density of ρ=k/r , k>0 , located between a sphere surface of r=a and another sphere surface of r=b, b>a. I'm supposed to find the electric field on all space, which I did. Now I have to find the electric potential in all space, which I also did for r>b...
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    Classical mechanics ~ Potential energy and periodic movement

    Hey all, suppose there's a particle with Potential Energy : U(x) = A*[ x^(-2) - x^(-1) ] , where A is a constant. I'm supposed to find the energy required to make the particle go from periodic movement to unlimited movement. First thing I did was U '(x) = 0 to find the balance points, now...