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Unformatted text preview: PHYS171 Final Exam Fall 2011 Name: _____________________ Student ID #: ________ 1 Short Answer Questions (respond in a few sentences using physical principals) (5 points each) 1) In the kinetic theory of gasses the temperature of the gas corresponds to the average kinetic energy per molecule and the pressure on the walls of a vessel enclosing a gas is due to collisions of the gas molecules with the walls. Describe why the temperature of a gas increases when it is compressed (assuming no heat exchanged with the environment). If the molecules bounce off a stationary wall they come off with the same kinetic energy. If they bounce off a wall which is moving towards them, they will have higher kinetic energy after the collision. Higher kinetic energy means higher temperature. 2) Consider two containers of gas. They contain the same number of atoms with the same temperature (the same kinetic energy per molecule). One container is larger. Which container has higher pressure and why? Larger container has lower pressure because molecules will have to travel a larger distance between collisions with the walls. They will collide with the walls less frequently, resulting in a lower rate of momentum transfer from wall to particles, and lower pressure. 3) Iron is more dense than water, yet a ship made of iron floats. Explain. (5 points) The iron boat is hollow. The volume displaced includes the empty volume. As long as the boat does not fill with water its mass is less than the mass of water it displaces. 4) A solid cylinder and a hollow cylinder roll down the same inclined plane. Which reaches the bottom sooner In the hollow cylinder average r 2 is larger, mass is concentrated farther from the axis. Equivalently, the moment of inertia of a hollow cylinder is larger than for a solid cylinder ( MR 2 vs MR 2 /2) There is more rotational energy for a given amount of linear center-of- mass energy. Therefore a smaller fraction of the potential energy change is transformed into linear energy. The hollow cylinder goes slower. PHYS171 Final Exam Fall 2011 Name: _____________________ Student ID #: ________ 2 5) You drop a lump of clay onto turntable spinning without friction on a rigid axle. In this process which of the following is conserved, mechanical energy, linear momentum, angular momentum. Since clay deforms, mechanical energy is lost. The turntable axle must exert force to hold the axis, so linear momentum is not conserved. Depite the external force, angular momentum calculated using the turntable axis is conserved because forces acting at the axis do not generate torque. 6) What is the percent change in the momentum of a particle that accelerates from speed 0. 9c to 0.95c? Give the result assuming classical physics, and assuming relativity....
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