Problems of the Week
These are the Problems of the Week. Some are easy, some are hard.
January 8th, 2007 An uncharged metal sphere of raduis R is placed in an otherwise uniform electric field E=E_o*zhat. Find the Potential outside the sphere.
January 20th, 2007 A spherical ball is falling at terminal velocity when it impacts the ground. It undergoes a perfectly elastic collision. What is the acceleration of the ball immediately after the collision? January 28th, 2007 What would the earth's orbit become if the sun's mass were instantly cut in half? (Classicaly) February 3rd, 2007 A comet starts at infinity, passes around a relativistic star of mass M and back to infinity. The impact parameter at infinity is b.The Schwartzschild radius of closest approach is R. What is the speed of the comet measured by a stationary observer at that point?
February 12th, 2007 Explain, in detail, why a radio station might have more than 1 antenna, if 1 antenna can be made as powerfull as any 2 or more antennas.
Febuary 21st, 2007 A small block, of mass m, is placed on top of a frictionless Sphere of Radius R, which is fixed to the ground. The block is given a small nudge so it is set into motion. How far away from the point where the sphere touches the ground does the block land?
February 24th, 2007 A spherical shell, of radius R, is carrying a uniform surface charge omega, it is spinning at an angular velocity omega. Find the magnetic field it produces at a point (r,theta,phi)
March 3rd, 2007 A sphere of radius R=4 is placed with its center at (0,0,5) and kept at voltage V=1, the infinite z=0 plane is kept at a voltage of V=0. Find the voltage in the region above the plane, and outside the sphere. Give your answer in cylindrical coordinates.
March 11th, 2007 Consider the Hamiltonian=1/2*p^2+1/2*(11(1+x^2)). Use Variational theory to find an upper bound on the ground state energy, taking hbar=m=1. If you can beat me, I will be very impressed! (I got E=0.281098) http://tinyurl.com/2lt2r7 for more info. March 18th, 2007 Consider a wire frame cube. Each edge has a resistance R. A battery of voltage V is connected to the cube at two corners that are diagonally across the cube from each other. What is the current through the battery? April 1st, 2007 Find an expression that discribes the Fraunhofer diffraction pattern resulting from illuminating a doughnut shaped aperature (by a plane wave), with Outer radius R and inner radius r. April 9th, 2007 You are at home, and you throw a ball up to a height of 10 meters. You then take a trip to your space station, in deep space. Its a large rotating cylinder of Radius R=1 mile, rotating so the centripital acceleration at R is equal to g. You throw the ball upwards with the same velocity that you did at home. What is the Maximum Height of the ball? July 27th, 2007 At t = 0, a hamster of mass m is placed on one edge of a platform inside a ring: What should be the hamster's path x(t) along the platform such that the ring doesn't rotate?
October 1st, 2007. POTW: A skier is moving along a hill y=h(x), and becomes airborne at (x_o, y_o), what was the skier's speed? You may assume the hill is C^inf.
