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Unformatted text preview: Chapter 8 Problems 1, 2 , 3 = straightforward, intermediate, challenging Section 8.1 Potential Energy of a System 1. A 1 000kg roller coaster train is initially at the top of a rise, at point A . It then moves 135 ft, at an angle of 40.0 below the horizontal, to a lower point B . (a) Choose point B to be the zero level for gravitational potential energy. Find the potential energy of the roller coasterEarth system at points A and B, and the change in potential energy as the coaster moves. (b) Repeat part (a), setting the zero reference level at point A . 2. A 400-N child is in a swing that is attached to ropes 2.00 m long. Find the gravitational potential energy of the childEarth system relative to the child's lowest position when (a) the ropes are horizontal, (b) the ropes make a 30.0 angle with the vertical, and (c) the child is at the bottom of the circular arc. 3. A person with a remote mountain cabin plans to install her own hydroelectric plant. A nearby stream is 3.00 m wide and 0.500 m deep. Water flows at 1.20 m/s over the brink of a waterfall 5.00 m high. The manufacturer promises only 25.0% efficiency in converting the potential energy of the water-Earth system into electric energy. Find the power she can generate. (Large-scale hydroelectric plants, with a much larger drop, are more efficient.) Section 8.2 The Isolated System Conservation of Mechanical Energy 4. At 11:00 AM on September 7, 2001, more than one million British school children jumped up and down for one minute. The curriculum focus of the Giant Jump was on earthquakes, but it was integrated with many other topics, such as exercise, geography, cooperation, testing hypotheses, and setting world records. Children built their own seismographs, which registered local effects. (a) Find the mechanical energy released in the experiment. Assume that 1 050 000 children of average mass 36.0 kg jump twelve times each, raising their centers of mass by 25.0 cm each time and briefly resting between one jump and the next. The free-fall acceleration in Britain is 9.81 m/s 2 . (b) Most of the energy is converted very rapidly into internal energy within the bodies of the children and the floors of the school buildings. Of the energy that propagates into the ground, most produces high frequency microtremor vibrations that are rapidly damped and cannot travel far. Assume that 0.01% of the energy is carried away by a long- range seismic wave. The magnitude of an earthquake on the Richter scale is given by...
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