9-26-08LectPHY2048

# 9-26-08LectPHY2048 - What is energy There is a fact or if...

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“There is a fact, or if you wish, a law, governing natural phenomena that are known to date. There is no known exception to this law ; it is exact, so far we know The law is called conservation of energy ; it states that there is a certain quantity, which we call energy, that does not change in manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity, which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number, and when we finish watching nature go through her tricks and calculate the number again, it is the same.” What is energy? Richard Feynman This “strange fact” is one of the most useful, foundational principles in all of physics.

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This could be determined by calculating the forces, accelerations and velocities at each point of the wire and carefully summing the latter to get v f but this would be quite tedious (or call for a computer, and effort to program it). Energy Methods The Newtonian methods we’ve learned are powerful and general, but there are circumstances in which they are extremely tedious to apply. Suppose a bead of mass m were sliding (without friction), on a wire bent as shown below and we ask what is its final velocity? i v G f v G
As we’ll see energy considerations let us handle this situation in a couple of lines. Part of what makes these methods a little hard to learn is that the terminology has seeped into our language and has a common usage that is in some sense meaningful, … First a word of warning: but ultimately too vague to be of use quantitatively. An example of this is provided by the word work . If somebody handed you a 50 kg cement bag and asked you to hold it for 30 minutes while they dug a hole you’d certainly say you were doing work. There would be effort involved, and you might rightfully want to get paid. But is work technically being done on the cement?

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Suppose there were a nearby ledge at the same height that you were handed the cement and you placed the bag there. Would you then be doing work on the cement? Should you be paid? Maybe (if only for having a little common sense). But no, you (obviously) would not be doing work on the cement. Moreover neither would the ledge. The ledge would apply a force to the bag, but it would not be transferring energy to the bag. This is the formal definition of work: work is the energy that is transferred to or from an object by a force acting on it.
In chapters 7 & 8 we begin to explore energy and the foundational principle of: The conservation of energy Energy is a conserved quantity in the sense that while its form may change, it is neither created nor destroyed.

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9-26-08LectPHY2048 - What is energy There is a fact or if...

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