Physics CS 33
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Set # 2
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Spring 2006
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| Due date |
Wed. April 19th
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Read HR&K:
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Chapter 16
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| Read
K&K: |
None
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| HR&K
Problems: |
Chapter 15 Problem 19
Chapter 16 Problems 3, 4, 8, 11,
14, 15
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K&K
Problems:
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None
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| 1. |
A raindrop has a
mass of one gram. Assuming it is perfectly spherical, find the
pressure of the water inside the raindrop. Use 1000 kg/m3
for the density of water and ignore the variation of pressure within
the drop due to gravity. You will have to look up the surface
tension of water. |
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| 2. |
Consider
the "Laplacian operator"  (i.e. the
divergence of the gradient)
a) Write out the Laplacian of φ in Cartesian coordinates.
b) Using index notation, show that  if φ is a "velocity potential" for an irrotational
flow. |
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| 3. |
Consider the "water-pressure
car" shown below:
Initially, the depth of the water is H. Assume A1
>> A2 , so the speed of water inside the tank is
small.
a) Find the thrust force as a function of h, the depth of the liquid at
any instant.
b) When all the water has drained out of the tank, what will the speed
of the car be?
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