Physics

The two blocks in the figure, of mass m and M respectively, are not attached, but there is a coefficient of static friction u between them. The surface below the heavier block M is frictionless. What is the minimum force magnitude F required to keep the smaller block m from slipping down? Express your answer in terms of m, M, u, and g.

Figure:
______
___| |
F-->| m | M |
|___| |
|______|

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asked by John
  1. Figure:

    ---------______
    -----___|------|
    F-->|-m-|--M---|
    ----|___|------|
    --------|______|

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    posted by John
  2. That's still not right but hopefully you can understand it. I wish it would just let me post a link to an image.

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    posted by John
  3. Leave spaces between the letters and numbers of the image web site and it should appear in your post

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    posted by drwls
  4. i . imgur . com/Ki7wM.jpg

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    posted by John
  5. on the whole system:
    F = (m+M)a
    on block m, call Fb the force between blocks:
    F - Fb = m a
    so
    (m+M)a - Fb = m a
    so
    Fb = M a
    for no slip:
    Fb u = m g
    Fb = m g/u
    M a = m g/u
    so
    a = (m/M) (g/u)
    so using F = (m+M)a
    F = (m+M)(m/M)(g/u)

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    posted by Damon

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