Lecture 18 - Physics and Astronomyphysics.unm.edu/Courses/Fields/Phys160/lecture15.pdf ·...
Transcript of Lecture 18 - Physics and Astronomyphysics.unm.edu/Courses/Fields/Phys160/lecture15.pdf ·...
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Lecture 18(Conservation of Energy)
Physics 160-01 Fall 2013
Douglas Fields
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Conservation of Mechanical Energy
• The work-energy theorem can be written as:
• And if there are no “other” forces doing work, then:
Other Gravity ElasticW KE U U
0
0
Gravity Elastic
Gravity Elastic
KE U U
E
E KE U U
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Problem 7.9
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Problem 7.24
k=1.06x104N/m
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Problem 7.46
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Problem 7.54
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Problem 7.75
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Forces from Potential Energy
• Since the potential energy is derived from the work as:
• Then, we can relate the Force to the derivatives of the potential energy function:
final final final
initial initial initial
x y zfinal
x y z
initial x y z
U W F ds F dx F dy F dz
, , , , , ,; ;x y z
U x y z U x y z U x y zF F F
x y z
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“Topological Map” circa 2009
35°10'49.43" N 106°28'09.65" W
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Energy Graphs
• One can learn a lot about the behavior of an object, just by looking at a graph of its potential and total mechanical energies.