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Determine the maximum ratio h/b

  1. Sep 12, 2016 #1
    Determine the maximum ratio $$h/b$$ for which the homogenous block will slide without toppling under the action of force F.The coefficient of static friction between the block and the incline is $$\mu_s$$.
    l5RXv.png
    I have a doubt.About which point should the rotational equilibrium be applied?Should it be applied about centre of mass?Or should it be applied about the vertex opposite to the vertex where F is applied?Why?

    **MY ATTEMPT:**

    **Translational Equations**
    $$F+mg\sin(\theta) \geq \mu N$$
    and $$N=mgcos(\theta)$$

    **Rotational Equations**
    This is where I'm facing a problem.Depending upon which point the equilibrium is applied the required ratio will be obtained.

    **MY VIEWS:**

    Rotational equilibrium should hold at all points if no toppling/rotation happens.However the answer varies depending on the point of application of equilibrium.Strange.
     
  2. jcsd
  3. Sep 12, 2016 #2

    haruspex

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    You are right that it would be strange. As long as you take all relevant forces into account properly, you should get the same answer. You must be making a mistake in one or other of your attempts.
    Please post those attempts.
     
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