Forces-Momentum

Forces-Momentum - Physical Sciences 2 Reading for Thursday,...

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Physical Sciences 2 Reading for Thursday, Sept. 17 1 Forces and Momentum At this point, we’ve talked a great deal about isolated systems. As you know, the total momentum of any isolated system—no matter how complex—is constant: For an isolated system, d dt ! p tot ( ) = 0 Although this fact about isolated systems is useful in those limited cases when we can treat a real system as approximately isolated, nearly all interesting systems are not isolated. Indeed, most real systems exhibit both internal and external interactions. As you recall, any system that participates in external interactions (interactions between an object inside the system and an object outside the system) is not isolated : system surroundings boundary in te rn a l external We now must consider how a system will behave if it is not isolated. Newton proposed that the time rate of change of the momentum of a system is equal to the net external force on that system. That is, he proposed: For a non-isolated system, d dt ! p tot ( ) = ! F ext ! (The symbol, which represents a sum, is a reminder that we are considering the net external force—i.e., the vector sum of all external forces—and not just any individual external force.) These forces , which change the momentum of a system, arise from the interactions between various objects. External forces arise from external interactions; internal forces arise from internal interactions. This proposal, that a net external force causes a change in momentum , is the heart of Newton’s system of mechanics and is indeed the original statement of Newton’s Second Law. Forces on a Single Object: Newton’s Second Law Usually in Newtonian mechanics, we will choose our “system” to consist of a single object; any system of more that one object can be broken down into several simpler systems,
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Physical Sciences 2 Reading for Thursday, Sept. 17 2 each of which has only one object. For a single object, of course, ! p = m ! v . (From our previous discussion, we know that the velocity ! v in this expression is the velocity of the center of mass of the object.) Thus, if our system consists of a single object, we can write: d ! p dt = ! F ext ! You should read this equation as “The time rate of change of the momentum of an object is equal to the net external force acting on that object.” This expression is close to Newton’s original statement of the second law: Lex II: Mutationem motus proportionalem esse vi motrici impressae et fieri secundum lineam rectam qua vis illa imprimitur. Law II: The rate of change of motion (momentum) of a body is proportional to the force acting on the body and is in the same direction . Although this equation may look unfamiliar, we can cast it in a familiar form if we turn it around and remember that we’re dealing with objects whose mass is essentially constant: !
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This note was uploaded on 03/14/2012 for the course PHYS SCI PS2 taught by Professor Loganmccarty during the Fall '10 term at Harvard.

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Forces-Momentum - Physical Sciences 2 Reading for Thursday,...

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