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Homework Help: Lateral Stress - need clarification

  1. Mar 27, 2010 #1
    1. The problem statement, all variables and given/known data

    (copied from a materials science assignment)

    During imaging the AFM tip may experience large frictional or adhesive forces or may come into contact with steep edges on the sample surface. Under these conditions AFM cantilevers are subjected to relatively large lateral forces and often brake. Assume the AFM cantilever shown in Figure 3 will break if it experiences a strain greater than ε = 0.002. Given that the lateral stresses are applied only in the direction of the cantilever length (along the [100] direction) what is the lateral force that will break the cantilever? (Assume that it breaks halfway along its length).

    There is no need to know about AFM or cantilevers, just the dimensions of the cantilever in question: Length 120 micrometers, width 30 micrometers, thickness 2.8 micrometers

    For the [100] crystallographic direction, the value of E, the modulus of elasticity is 129.5 GPa.

    2. Relevant equations

    Stress = Force/area
    Stress = E*epsilon = young's modulus times strain

    3. The attempt at a solution

    Calculating the stress is straightforward = 129.5 GPa times 0.002 which is 259 MPa.

    But where I'm confused now is what value I should use for the area so I get the force, since I need to multiply the stress by the area.

    Since the question says the lateral stress is along the length, I thought that maybe the force is applied at the short end of the cantilever - so the area would be 30x2.8 square micrometers.

    But my friends disagree and say that the force is applied at the long end so the area is 120x30 square micrometers.

    Which one is right? The question is not clear so I am really uncertain as to which value of area I should use. Once I have that I can calculate the force very easily.
  2. jcsd
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