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Unformatted text preview: Physics 15a, Fall 2006 Final Exam, 1/20/07 1. A spring with spring constant k and relaxed length L stands vertically on the ground, with its bottom end attached to the ground. A mass m is attached to the top and lowered down to the ground, so that the spring is compressed to zero length. The mass is then released from rest and accelerates vertically upward. What is the maximum height above the ground it reaches? You may assume that k > mg/L , so that the mass does indeed rise up off the ground. Note that at all times, the mass remains attached to the spring, and the spring remains attached to the ground. (If you group things wisely, you can avoid solving a quadratic equation.) 2. In the Atwoods machine shown below, the pulleys and strings are massless, and both masses are m . Find the accelerations of the masses. m m 3. (Relativity) Two people holding paint brushes stand on the ground, a distance L apart as measured in the ground frame. A stick moves past them at speed v , as shown. At a given moment, the people simultaneously (as measured in the ground frame) paint little marks on the stick. Let L be the distance between the marks, as measured in the stick frame. (a) By working in the ground frame, find L ....
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