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Force to break one, two and three white pine boards

  1. Feb 26, 2013 #1
    1. The problem statement, all variables and given/known data
    Assume you have 6 white pine boards with all the same breaking force and there is no difference in the boards at all

    If you find the force to break one pine board, two pine boards with no gaps and three pine boards on top of each other with no gap.

    Does the amount of force required to break two and three pine boards increase linearly e.g) two pine boards required two times the amount of force to break then one board and three pine boards require three times the amount of force to break one pine board? Explain your answer.

    Also if you have two white pine board but you have a small gap in between them and break them, does it require more or less force to break it then two pine boards with no gap between them? Explain your answer

    2. Relevant equations

    Can't find any

    3. The attempt at a solution

    At the start i assumed that the force to break two and three white boards would be two and three times the force to break one board
    e.g.) if it takes 1100 Newtons to break one pine board, then about 2200 newtons to break two boards and 3300 newtons to break three boards.

    I have done an experiment on this to test it but the values i get are along the lines of:
    1 board -> 1100 Newtons
    2 boards -> 2500 Newtons
    3 boards -> 4900 Newtons

    2 boards with 3.5mm gap -> 2300 Newtons.


    I cannot find a reason why the force to break the 2/3 boards is more than twice/triple the force to break one board

    Also for the 2 boards with and without a gap I assumed that it would be easier to break it with a gap because of the when the top board breaks, each half board gets an angular momentum which then gets imparted on the next board which would make it easier to break.



    I need help with explaining the first part of the question. Any help would be greatly welcomed :)
     
  2. jcsd
  3. Feb 26, 2013 #2

    mfb

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    Staff: Mentor

    How do you apply your force? If you apply it to the upper board only, how does that upper board applies a force on the lower board?
    Do you see a difference?
     
  4. Feb 26, 2013 #3
    Often, you can justify results that you don't understand by looking at another, more extreme example. Imagine, instead of three boards, you have many thin pieces of paper. Imagine the force required to cut through them separately, and together, just like the boards. What would you assume would be the difference, and why?

    Also, as mfb states, think about the transfer of force between the boards. A free body diagram may be useful.
     
  5. Feb 26, 2013 #4
    First consider what would happen if, when you had two boards and three boards, you glued the boards together with superglue. In these cases, you would form a single thicker board with twice or three times the thickness. In beam bending, the highest tensile stress resides on the outside of the bend. Do you know how to determine the tensile stress on the outside of the bend? For a fixed loading, how does it vary with the thickness of the beam? In your case, how would it vary with the number of boards you glued together? Would it vary with the number of boards to the first power, the second power, or ??? What you are doing when you glue the boards together is preventing them from sliding relative to one another. This should give you some idea what is happening when the boards are not glued together.

    Next consider the case in which, instead of gluing the boards together, you put butter or some other slippery lubricant between the boards, so that they can not sustain shear stresses at their interfaces. What happens here?
     
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