Douglass Houghton Workshop, Section 1, Wed 11/30/11
Worksheet Partridge
1. (This problem appeared on a Winter, 2008 Math 115 exam) A
bellows has a triangluar frame made of three rigid pieces. Two
pieces, each 10 inches long, are hinged at the nozzle. They are
attached to the third piece at points
A
and
B
which can slide,
as shown in the diagrams below. (The Fgures show a 3D sketch
of the bellows and a 2D sketch that may be speciFcally useful
to solve the problem.)
Each piece of the frame is 2 inches wide, so the volume (in cubic
inches) of air inside the bellows is equal to the area (in square
inches) of the triangluar crosssection above, times 2. Suppose
you pump the bellows by moving
A
downward toward the center
at a constant speed of 3 in/sec. (So
B
moves upwards at the
same speed.) What is the rate at which air is being pumped out
when
A
and
B
are 12 inches apart? (So
A
is 6 inches from the
center of the vertical piece of the frame.)
b
b
b
nozzle
A
B
h
10
10
b
2. (This problem, like all Awkward Turtle problems, appeared on a Winter 2009 Math 115
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 Winter '08
 Conger
 Math, Inch, Bellows, Awkward Turtle, Dragana

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