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Day 3.5 Conservation of Energy and Electricity 1) An electron is released between two parallel oppositely charged plates. Sketch the energy bar diagrams (in the order K,E, T) when the electron a) has not yet been released b) is 1/3 of the way across c) is 1/2 of the way across d) is all the way across e) How is this similar to and different from dropping a ball? f) Calculate how fast it will be moving after 4.2 cm if the electrical field strength is 350 N/C. Hint: How would you solve this, if it were a ball dropping? 2) Two carts are held together against two repelling magnets and then released. Assume friction is negligible and sketch the energy bar diagrams for kinetic, magnetic and total energy when the cart is a) Not yet released. b) Released but still close. c) Really far apart. d) http://phet.colorado.edu/en/simulation/efield Simulate this problem with two positive charges. Set the field as low as possible and add two charges. e) Suppose the carts each have a mass of 1.3 kg and their top speed was 0.9 m/s. How much energy was stored in the magnetic field? . 3) A proton is heading directly toward a gold nucleus. (Atomic number = 79). Sketch the energy bar diagrams when it is a) really far away b) closer c) at minimum distance d) Sketch the paths of 3 alpha particles moving parallel to each other with the same speed toward a gold nucleus. Add arrows to show the speeds at different points and explain your reasoning using conservation of energy. Check this with stretchy fabric and http://phet.colorado.edu/en/simulation/rutherford-scattering e) The equation for gravitational potential energy is E = -GMm/r. What should the equation for electrical potential energy be? f) Calculate the closest approach of an alpha particle moving at 1 x 107 m/s toward a gold nucleus. q1 = 2e, q2 =79e, m = 6.64 x 10-27 kg. g) Rutherford Gold Foil Experiment http://www.backstagescience.com/videos/rutherford_gold_foil.html Why was the experiment so important and so tedious to do? 4) The LHC (Large Hadron Collider) fires protons at each other. Suppose the protons are moving at 0.75 c, how close will they get to each other? (The protons will actually be going more like 0.99999c.) Look at Oxford Sparks: A quick look around the LHC. http://www.youtube.com/watch?v=BEnaEMMAO_s Textbook: 7.6 p. 371 #2, 3, 4 p. 377 # 12, 13, p. 379 # 22, 34,