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Statics, continued

Explore the tipping-over conditions of a box on a ramp and two book configurations. Determine which cases result in tipping over and understand the role of center of mass.

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Statics, continued

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  1. Statics, continued November 7, 2005

  2. 80 1 2 3 5 0 0 A box is placed on a ramp in the configurations shown below. Friction prevents it from sliding. The center of mass of the box is indicated by a blue dot in each case. In which cases does the box tip over ? • All • 1 only • 2 only • 3 only • 2 and 3

  3. 60 5 0 0 Consider the two configurations of books shown below. Which of the following is true? • Case 1 will tip • Case 2 will tip • Both will tip • Neither will tip 1 2 1/4 1/2 1/2 1/4

  4. Answers • The torque due to gravity acts like all the mass of an object is concentrated at the CM. Consider the bottom right corner of the box to be a pivot point. If the box can rotate such that the CM is lowered, it will, so the answer is #4, “3 only” • The CM of the system is midway between the CM of each book. Therefore, the CM of case #1 is not over the table, so it will tip. The answer therefore is #1.

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