Mp hw09a - MasteringPhysics: Assignment Print View Page 1...

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IUPhysicsP201F2009 Assignment09a Due at 11:00pm on Tuesday, October 28, 2008 Assignment Display Mode: View Printable Answers View Grading Details Torques on a Seesaw: A Tutorial Description: Balancing seesaw: intuition, how it relates to torque, and finally balancing using horizontal force. (version for algebra-based courses) Learning Goal: To make the connection between intuitive understanding of a seesaw and the standard formalism for torque. This problem deals with the concept of torque, the "twist" that an off-center force applies to a body that tends to make it rotate. Use your intuition to try to answer the following question. If your intuition fails, work the rest of the problem and return here when you feel that you are more comfortable with torques. Part A Marcel is helping his two children, Jacques and Gilles, to balance on a seesaw so that they will be able to make it tilt back and forth without the heavier child, Jacques, simply sinking to the ground. Given that Jacques, whose weight is , is sitting at distance to the left of the pivot, at what distance should Marcel place Gilles, whose weight is , to the right of the pivot to balance the seesaw? Hint A.1 How to approach the problem Consider whether increases or decreases as each of the variables that it depends on, , , and , is made Page 1 of 13 MasteringPhysics: Assignment Print View 9/17/2008 http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1142221
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Now consider this problem as a more formal introduction to torque. The torque of each child about the pivot point is the product of the child's weight and the distance of the child (strictly speaking, the child's center of mass) from the pivot. The sign of the torque is taken to be positive by convention if it would cause a counterclockwise rotation of the seesaw. The distance is measured perpendicular to the line of force and is called the moment arm . Marcel wants the seesaw to balance, which means that there can be no angular acceleration about the pivot. For the angular acceleration to be zero, the sum of the torques about the pivot must equal zero: . Express your answer in terms of , , and . larger or smaller. ANSWER: = Part B Find the torque about the pivot due to the weight of Gilles on the seesaw. Express your answer in terms of and . ANSWER: = Part C Determine , the sum of the torques on the seesaw. Consider only the torques exerted by the children. Express your answer in terms of , , , and . If you did not solve for the distance required to balance the seesaw in Part A, do so now. The equation applies to any body that is not rotationally accelerating. Combining this equation with (which applies to any body that is not accelerating linearly) gives a pair of equations that are sufficient to form the basis of statics . The art of applying these equations to large or complicated structures Hint C.1 Torque from the weight of the seesaw The seesaw is symmetric about the pivot, and so the gravitational force on the seesaw produces no net torque. More generally, when determining torques, the gravitational force on an object in a uniform gravitational field
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