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Chapter
2: Understanding Variables and Solving Equations
Numbers in the Real World |
Motor Math
Ferrari Testarossa, Lamborghini Countach, Porsche 911, and Chevrolet
Corvette. Those are some of the names that car enthusiasts go crazy
over. These cars all have classy looks, but they also have what car
lovers crave....SPEED. The maximum speed of a car depends on a number
of factors, one factor being engine displacement.
In an engine, displacement is the total volume of air and fuel that
an engine is theoretically capable of drawing into all its cylinders in
one cycle. Since an engine is three-dimensional (volume), displacement
is measured in cubic inches for U.S. cars. Some cars may have displacements
measured in liters.
Displacement is computed as follows:
As you can see, displacement depends on
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the number of cylinders C
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the length of the stroke S
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the diameter of the cylinders D
(also called the bore)
Since each of these variables are being multiplied in the expression, the
only way to increase displacement is to increase any or all of these.
You may have heard of "boring out" an engine. This widening of the
cylinders increases the diameter of the cylinders D,
thus increasing the displacement. Many car manufacturers have
increased the number of cylinders as well.
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Chevrolet Corvette C5
The new C5, introduced in 1997, has 8 cylinders, a bore size of 3.8976
in, and a stroke length of 3.6620 in. |
Ferrari F512M
The F512M, the evolution of the Testarossa, was introduced in 1995.
The sportster has 12 cylinders, a bore size of 8.2 cm, and a stroke of
7.8 cm. |
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Porsche 911
The 911 has 6 cylinders, a bore size of 9.60 cm, and a stroke length
of 7.80 cm. |
Chevrolet Metro Coupe
The Chevrolet Metro has 4 cylinders, a bore size of 2.91 in, and a stroke
length of 3.03 in. |
Let's compute the displacement of the Chevrolet Corvette C5.
Substituting 8 for C, 3.8976 for B, and 3.6620 for S yields
or 349 cubic inches
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Compute the displacement for the other 3 vehicles.
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Write each displacement in both cubic inches and liters, using the following
relationships:
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1,000,000 cubic millimeters = 1,000 cubic centimeters = 1 liter
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1 inch = 2.54 centimeters or 1 cubic inch = 2.543
cubic centimeters
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Look up your favorite automobile on the Internet and find its engine specifications.
Verify that the displacement listed is correct.
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Analyze the expression that represents displacement. Using the fact
that 3.14 is an approximation for pi, explain why the expression is valid.
Hint: Look at the definition of engine displacement above.
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