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Unformatted text preview: 10/26/09 Professor Philip S. Marcus ME106 Problem Set 7 Due in class Friday October 30, 2009 O1) We are now experts in rockets and in driving trucks with chickens across bridges. We are prepared therefore to combine the two together. According to our class lectures, we learned that a bridge that can support a two ton load before collapsing, will collapse if you cross that bridge driving a truck weighing 1.5 tons carrying 1 ton of chickens resting on the floor of the truck. We also learned that the bridge will collapse if, before crossing the bridge, you get your chickens flying, so that they are not resting on the floor, but flapping their wings such that they maintain a steady elevation inside the truck. (We assumed that the truck was airtight, but didnt asphyxiate the chickens.) Then we learned that if you immobilized the chickens (i.e., froze them), you could cross the bridge without it collapsing. The trick was to attach the chickens to the ceiling of the truck, and just as the truck started to cross the bridge cut them free from the ceiling, letting them drop under the influence of gravity so that they accelerated downward at a rate equal to g , the local acceleration of gravity. (The journey over the bridge had to be completed before the chickens hit the floor of the truck.) We learned, in fact, that with this situation of freely-falling chickens, you could successfully cross a bridge that would support a 1.5 ton load, i.e, the weight of the empty truck . 1 This phenomenon raises the question: If the chickens moved downward at an acceleration faster than g , could you drive across a bridge that supported only a 1.4 ton load (less than the weight of an empty truck)? Lets consider three versions of this problem. In each case we shall place rocket-propelled back-packs on the chickens. a) In the first experiment, as you begin to cross the bridge, the chickens are all hovering under their own power, just below the ceiling of the truck. As you begin your journey across the bridge, the chickens start their rocket engines so that the exhaust from the rockets is propelled straight-upward and the chickens fly straight downward. Assuming that you cross the bridge before the chickens hit the floor, what are the conditions (if any) that the chickens rockets need to satisfy? We shallwhat are the conditions (if any) that the chickens rockets need to satisfy?...
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This note was uploaded on 04/19/2010 for the course ME 106 taught by Professor Morris during the Fall '08 term at University of California, Berkeley.
- Fall '08