Slinky Secrets Revealed

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Math Lab 23

• Slinky Secrets Revealed

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Purpose of Lab

• Demonstrate that the force used to stretch a
  spring is proportional to the amount it
  stretches. Find the constant of proportionality.

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Math Principles

• Direct variation, scatter-plot, slope, measuring
  with a ruler, linear regression.

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What Its All About

• The amount of force (F) needed to stretch a
  spring varies directly as the amount of stretch
  (x). The equation that describes this is
• F (const)x.

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What Its All About

• In this lab the stretching force is provided by
  the weight of nuts hung on the end of a spring
  (slinky). Since this weight is proportional to
  the number of nuts, the equation will be modified
  to the following where N is the number of nuts
• N kx

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What Its All About

• Marks will be made on the background (chalk board
  or white board) as several nuts are successively
  placed on the hanger. Distances between the marks
  are measured for later analysis in which the
  constant of proportionality will be determined.

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Slinky Secrets Revealed

• Mark the starting point With the spring hung
  with no added weights, stabilize it and mark the
  bottom of the spring. All measurements will be
  referenced from this point. Make sure the student
  marking this and following positions has his eyes
  level with the bottom of the spring so as to
  accurately mark the true position.

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Slinky Secrets Revealed

• Gently hang one nut on the hanger, stabilize the
  spring, mark the position, and label with 1.
  Again, make sure eye level is at the bottom of
  the spring so as to place an accurate mark.

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Slinky Secrets Revealed

• One at a time, add nuts (up to a total of four)
  to the hanger. Each time mark the position of the
  bottom of the spring and record the number of
  nuts beside each mark. The picture below shows
  the marks and labeling after all four nuts have
  been attached.

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Slinky Secrets Revealed

• Measure the distances Using a centimeter ruler,
  measure the distances of each position of the
  spring (1, 2, 3, 4) from the zero mark as shown
  to the left.

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Slinky Secrets Revealed

• Putting it all together Make a scatter-plot of
  the points with a large black marker.

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Slinky Secrets Revealed

• Finding the constant of proportionality
  Determine the constant of proportionality (k,
  also the slope of the line) for this line as
  follows

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Slinky Secrets Revealed

• Finding the constant of proportionality
  Determine the constant of proportionality (k,
  also the slope of the line) for this line as
  follows
• Since the line goes through the origin, use (0,
  0) as one point and (36.4, 4) as the other. The
  slope (and therefore k) is

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Slinky Secrets Revealed

• Finding the constant of proportionality
  Determine the constant of proportionality (k,
  also the slope of the line) for this line as
  follows
• Since the line goes through the origin, use (0,
  0) as one point and (36.4, 4) as the other. The
  slope (and therefore k) is

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Slinky Secrets Revealed

• Finding the constant of proportionality
  Determine the constant of proportionality (k,
  also the slope of the line) for this line as
  follows
• Since the line goes through the origin, use (0,
  0) as one point and (36.4, 4) as the other. The
  slope (and therefore k) is

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Slinky Secrets Revealed

• Finally, the complete linear function is
• F .10989x