What do cantilevers and pulling nails have in common?

cantilever
Math Standard:
A.CED.1 Create equations in one variable and use them to solve problems.
G.CO.2 Represent transformations.
CTE Standard:
            Students will understand how levers and fulcrums are used in construction.
Teacher Notes/Materials Needed:
Ruler, cups, fulcrum, fun size candy bars, 2 x 10 x 10,
CTE Situation (opener):
What principle is involved in deciding how far you can cantilever a deck or 2nd floor, or how big a hammer or crow bar is needed to pull a nail?  Why is holding a hammer close to the head less efficient than holding it close to the end of the handle?
Lesson Sequence:  Can 1 candy bar lift 6 candy bars?
1.     Show a visual demonstration of the lever/fulcrum principle by using a ruler, pen (fulcrum), 2 plastic cups, fun size candy bars.  Model this with the fulcrum at the center of the ruler with a cup containing 1 candy bar placed on one end of the ruler and a cup containing 6 candy bars on the other end (note it does not balance).
a.     Discuss and experiment with ruler lever/fulcrum so that 1 candy lifts 6 candies.
b.     An extension, using a 2 X 10 x 10, have a lightweight student lift a larger (football player type) student.

c.      Process with students using the photos above, where is the fulcrum and lever located?  This is a great place to talk about the “center of rotation” and “translation” of the fulcrum.

fulcrum
2.     Transition into developing a math expression/equation to represent the lever scenario

 
longer distance X lighter person = shorter distance X heavier person
or express as a proportion
Thanks to John Gregory & Steven Davis of Norwich, NY for letting this problem be reprinted.
1 Comment
  • Essem Engineers
    Posted at 05:00h, 17 April Reply

    Your articles about cantilever lifts will certainly enlighten us with the knowledge.

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