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Two stacked blocks attached to a spring

  1. Apr 20, 2014 #1
    1. The problem statement, all variables and given/known data
    ehhpjo.png


    2. Relevant equations
    F_spring = kx, where x is the distance compressed
    f_friction = uN


    3. The attempt at a solution
    Forces acting on m: N_1 up, mg down, f_friction to right
    Forces acting on M: N_2 up, Mg+N_1 down, f_spring to the right

    Block m will still be in equilibrium as long as the force exerted by the spring equals the force of friction:

    kx = uN_1
    The block isn't accelerating in y-direction so N_1 = mg
    So kx = u*mg
    x = u*mg/k

    Does that look fine?
     
  2. jcsd
  3. Apr 20, 2014 #2

    Pythagorean

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    Looks good to me, force balance between the friction and the spring gives the upper bound.

    A small nitpick; I might have worded this differently:

    "Block m will still be in equilibrium as long as the force exerted by the spring equals the force of friction:"

    I would instead say "is equal to or less than".
     
  4. Apr 21, 2014 #3

    haruspex

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    No, this is wrong. You've not taken into account that the spring also has to accelerate M, so the accelerating force on m will be less than kx.
    Let the acceleration be a. Write out the horizontal ∑F=ma equations for both blocks. Don't forget that the horizontal friction force on m applies equally and oppositely to M.

    First, we're not asking for m to be in equilibrium - merely that it does not slip.
    Secondly, the condition for not slipping is that the horizontal force required to accelerate it at the same rate as M does not exceed the maximum frictional force. The actual frictional force may be less than maximum.
     
  5. Apr 21, 2014 #4

    Pythagorean

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    Ugh, thanks haruspex. I'm more disconnected from this stuff than I thought.
     
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