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    Proving an equation is an eigenstate of the momentum operator.

    Homework Statement A free particle (de Broglie wave) may be represented by the wave-function \psi(x)=Aeikx Show that this is an eigenstate of the momentum operator \hat{p}=-\hbar\frac{\delta}{\deltax} Homework Equations \hat{p}un(x)=anun(x) an is the eigenvalue un(x) is the corresponding...
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    Calculating ratio energy radiated in a loop and comment on result

    Homework Statement Designers of electrical circuits often take the maximum amplitude of the radiated electric field (at a large distance r) produced by an alternating current I0 flowing in a loop of area A cm2 to be given by E=\frac{2.6AI0f2}{r}\muVm-1 where f is the frequency in MHz...
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    SHM question involving a tunnel through earth

    Homework Statement A tunnel is bored through the centre of the Earth from Liverpool to New Zealand and a travel pod is dropped into it. The gravitational force on the pod is proportional to its distance from the centre of the Earth and so it undergoes simple harmonic motion described by...
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    Create a wave equation with the following properties.

    Homework Statement Write down an equation to describre a wave \psi(x,t) with all of the following properties a) It is travelling in the negative x direction b) It has a phase velocity of 2000ms-1 c) It has a frequency of 100kHz d)It has an amplitude of 3 units e) \psi(0,0)= 2 units...
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    Bohr Quantisation Question

    Homework Statement The ionisation energy of a single hydrogen atom is 13.6 eV. The application of Bohr quantisation to the hydrogen atom results in the stationary states having discrete energies given in terms of a positive integer n according to E=-RB/n2 where RB is the Rydberg...
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    Frequency and Intensity Level of Sound Waves

    (b) The frequency of sound waves received by a detector when both source and detector move relative to the air is: f=f0[u(+ or -)vd/u(+ or -)vs] . Two trains are approaching each other at a level crossing and blow their whistles at a frequency of 500 Hz. Train 1 is travelling at 20% of the...
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    Displacement of a Transverse Wave on a String Question

    Homework Statement Question 1 (a) The displacement of a transverse wave on a string is described by: y(x, t) = 0.01 sin(4x + 200t + \pi), where all quantities are expressed in SI units. i) Determine values (with appropriate units) for the period, wavelength, and phase velocity of the wave...
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    Electricity and Magnetism Question

    Homework Statement The potential caused by an array of charges in a region of space can be described by the equation V(x,y,z)=2x+xy+y2-xz2 volts, where all distances are measured in metres. If a charge of 2 mC is moved from the position r1=(1,2,0)m to r2=(3,1,0), calculate the resulting change...
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    Electrostatic Force Question

    Homework Statement During a collision between two initially uncharged polystyrene balls of radius 2 mm, some electrons are transferred from one of the balls to the other. In what direction does the resulting electrostatic force between the balls act? The magnitude of the force between the...
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    Keplers Third Law Question

    Homework Statement Assuming that the orbits of the Earth, and of Jupiter, around the Sun are circular and given that Jupiter orbits with a radius 5.2 times that of the Earth, calculate the orbital period of Jupiter around the Sun. Homework Equations T2=(4(pi)2/(G*M))*r3 The Attempt...
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    Momentum and Kinetic Energy Question

    Homework Statement Two bodies approach each other with the same speed of 2 m/s and collide head-on in an inelastic collision. The mass of one body is m, the other has mass 3m. After the collision, the lighter body has rebounded to travel back along its original trajectory with speed 1 m/s. (i)...
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    Coefficient of Kinetic Friction Question

    Homework Statement A box is held on a rough plank inclined at an angle of 60° to the horizontal. The box is released from rest and slides down the plank with a constant acceleration of 5 m/s2. Calculate the coefficient of kinetic friction between the box and the plank. Homework...
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    Static Friction Question

    Homework Statement A crate resting on a rough plane is found to be on the verge of sliding when the plane is inclined at an angle of 40 degrees to the horizontal. Calculate the coefficient of static friction between the crate and plane. [ Homework Equations f(s)<_(Mu(s))N <_ is meant to...
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    Drag (Turbulent Flow) Question

    Homework Statement A projectile of mass 0.1 kg travelling horizontally through the air with speed v(t) experiences a drag force DT (t) whose magnitude is given by: D (t ) 0.001 [v (t )] 2 At one instant, the projectile’s speed is measured to be 100 m/s. Calculate the speed of the...
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