ch10-dynamics-of-rotational-motion

ch10-dynamics-of-rotational-motion - MasteringPhysics...

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11/17/08 11:47 PM MasteringPhysics Page 1 of 14 http://session.masteringphysics.com/myct [ Print View ] Introductory mechanics Chapter 10 - Dynamics Of Rotational Motion Due at 11:59pm on Tuesday, November 18, 2008 View Grading Details Torques on a Seesaw: A Tutorial Learning Goal: To make the connection between your 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. Try to use your intuition 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 A mother is helping her children, of unequal weight, to balance on a seesaw so that they will be able to make it tilt back and forth without the heavier child simply sinking to the ground. Given that her heavier child of weight is sitting a distance to the left of the pivot, at what distance must she place her second child of weight on the right side of the pivot to balance the seesaw? Hint A.1 How to approach the problem Hint not displayed Express your answer in terms of , , and . ANSWER: = The figure shows the seesaw slightly tilted, as will be the case when in use. This does not change the torque balance because the horizontal distances from the pivot to each child (which are called the moment arms for the vertically directed weight and must be used to calculate the torque instead of the distance along the seesaw) are reduced equally, so the sum of the torques is zero at any angle. Given that the torque is zero at all times (except when one or both children push on the ground), there will generally be no angular acceleration of the seesaw, and the seesaw will rotate at a constant velocity between pushes from the feet of the children on the ground. 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 positive 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 . [ Print ]
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11/17/08 11:47 PM MasteringPhysics Page 2 of 14 http://session.masteringphysics.com/myct The concept of torque requires both a force and a specification of the pivot point, emphasized by the first subscript on the torque. Part B Find , the torque about the pivot due to the weight of the smaller child on the seesaw. Express your answer in terms of and . ANSWER: = The children's mother wants the seesaw to balance, which means that there can be no angular acceleration about the pivot. The balanced seesaw will then be in equilibrium since it has neither linear acceleration nor rotational acceleration. For the linear acceleration to be zero, the vector sum of forces acting on the seesaw and children must equal zero.
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This note was uploaded on 04/07/2010 for the course PHYS 3163 taught by Professor Pickett during the Spring '10 term at CSU Long Beach.

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ch10-dynamics-of-rotational-motion - MasteringPhysics...

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