ex2-2005-sol

ex2-2005-sol - MasteringPhysics 2.0: Assignment Print View

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MasteringPhysics 2.0: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrint?assignmentI. .. 1 of 8 02/11/2005 14:27 Assignment Display Mode: View Printable Solutions Class WARWICK2005 PX132 Mechanics Assignment 2 (NOT assessed) Assignment is due at 5:00pm on Monday, November 14, 2005 Credit for problems submitted late will decrease to 0% after the deadline has passed. There is no penalty for wrong answers to free response questions. Multiple choice questions are penalized as described in the online help. The unopened hint bonus is 2% per part. You are allowed unlimited attempts per answer. A Gymnast on a Rope Description: A gymnast climbs up and down a massless rope. Find the tension in the rope, given the weight, velocity, and acceleration of the gymnast. A gymnast of weight climbs a vertical rope attached to the ceiling. You can ignore the weight of the rope and assume that the rope does not stretch. Part A Calculate the tension in the rope if the gymnast climbs at a constant rate. Hint A.1 A body in dynamic equilibrium The gymnast is moving at a constant rate, that is, with constant velocity. This means that the gymnast is in dynamic equilibrium and, according to Newton's 1st law, the net force acting on the gymnast is zero. ANSWER: = w Part B Calculate the tension in the rope if the gymnast hangs motionless on the rope. Hint B.1 A body in static equilibrium The gymnast is hanging motionless, that is, at rest. This means that the gymnast is in static equilibrium and, according to Newton's 1st law, the net force acting on the gymnast is zero. ANSWER: = w Does it surprise you that the answers to Parts A and B are identical? In both cases, the gymnast is not accelerating. Therefore there must be zero net force acting on the gymnast. Since the only two forces acting on the gymnast are tension and weight, the tension in the rope in each case is equal in magnitude (and opposite in direction) to the gymnast's weight. Part C
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MasteringPhysics 2.0: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrint?assignmentI. .. 2 of 8 02/11/2005 14:27 Calculate the tension in the rope if the gymnast accelerates up the rope with an acceleration of magnitude . Let be the mass of the gymnast. Hint C.1 Newton's 2nd law of motion According to Newton's 2nd law, if a body accelerates, the net external force acting on it is equal to the mass of the body times the acceleration of the body: . Part C.2 Find the net external force The only forces acting on the gymnast are the upward force of the rope on the gymnast (the tension in the rope) and the downward force of the gynmast on the rope (the weight of the gymnast). Find an expression for the net external force acting on the gymnast while accelerating up the rope. Take the positive y axis to be upward.
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ex2-2005-sol - MasteringPhysics 2.0: Assignment Print View

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