Unformatted text preview: Physics 7A Final Examination. Section 3. A. Zettl, Spring 2003. All problems worth 20 points each.  . , _ one Atmenstunql
l. A thin rod of length L is cast from a metal alloy in such a way that It has a nonunifomg mass density 9» along its length: A: A + Bx4, where A and B are constants and x is measured from the middle of the rod. The
rod is rotated at constant angular speed to about an axis perpendicular to the rod and passing through the center of the rod. Determine the magnitude of the angular momentum the rotating rod. Kaf AI‘CA o‘c Co 'ha. :
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Large KARL 2. A cylindrical block of wood (density p1) of cross sectional area A1 and height L ﬂoats in a tank of ﬂuid
(density p2). The tank has cross—sectional area A2. You push down a bit on the block and then let go, and the
block is observed to bob up and down on its own. Determine the angular frequency a) of the block's up and
down oscillations, assuming in turn the following conditions:
a) that the tank holding the ﬂuid has an extremely large crosssectional area (i.e. A2>>A1) 33gb) that the cross—sectional area of the tank is not much larger than A1. This means that the ﬂuid level is not constant as the block oscillates. 3. A model for a onedimensional solid is a series of identical point masses in (representing the atoms)
connected by identical springs of spring constant k and length L (representing the bonds between atoms).
a) Estimate the speed of a longitudinal (compressional) wave travelling through such a solid. [Hint Your
answer will contain m, L, and k. Recall the method we sometimes used in class to attack rather difficult problems] A m .It m ,k
 . ' 1% M Jl M k M C . .  .. . V?) vT—J v V‘— ""’ a}: '
4. You (of mass m) have just climbed to the top of a tall, thin, uniform ﬂagpole (of length L and mass M)
when it cracks at its base and begins to topple over (the cracked base serving as a frictionless hinge). You
decide to either a) let go immediately and "free—fall" to the ground, or b) hang on to the tip and ”ride" the pole
all the way to the ground. Assuming the criterion for minimum injuries is minimum speed v with which you
hit the ground, determine which is the safer choice, a) or b). Do not make any assumptions about the relative ma nitudes of m and M i.e. the ma be com arable .
g ( y y p ) “VI/Y6 v=lm/Sec AVB All) m I: ((4) 4%) \ S) . "MA/s“ BaC
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{ﬂ A ”'7'”? ’3‘ 5. A nervous monkey races around inside his cage, over and over. The path the monkey takes is indicated in
the figure—— all motion is in the xy plane. At time t=0 the monkey starts at the origin at A and runs with a
constant speed v=1m/s across the ﬂoor to point B (at x=1m, y=0). Then he immediately climbs the curved
front of the cage (a quartercircle, with radius R =lm), again moving at constant speed v=1m/s up and over to
C (at x=0, y=1m) where he instantly stops and then immediately "free falls", dropping to the ground at A,
whereupon he immediately runs from A to B again, etc. He is bored out of his mind and would happily trade
places with you right now. a) Determine the round—trip time T for the monkey in going from A back to A. b) Make quantitative plots of the velocity vector components vx and vy for the monkey, from t=0 to t=T. Keep track of positive and negative quantities.
c) Make quantitative plots of the acceleration vector components ax and ay for the monkey, from t=0 to t=T. Keep track of positive and negative quantities. ...
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 Spring '08
 Lanzara
 Physics

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