Will the Block Tip Over or Slip on an Incline?

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A uniform rectangular wood block on an incline will either tip over or slip at a critical angle determined by its dimensions and the coefficient of static friction. The relationship between the block's height (a), length (b), and static friction coefficient (µs) is crucial, with the condition for tipping being µs > b/a. The block tips when the vertical line through its center of mass falls outside its base of contact with the incline. Understanding these dynamics is essential for solving the problem effectively. The discussion emphasizes the importance of analyzing the forces at play to determine tipping versus slipping conditions.
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Homework Statement


A uniform rectangular wood block of mass M, with length b and height a, rests on an incline as shown. The incline and the wood block have a coefficient of static friction, µs. The incline is moved upwards from an angle of zero through an angle θ. At some critical angle the block will either tip over or slip down the plane. Determine the relationship between a, b, and µs such that the block will tip over (and not slip) at the critical angle. The box is rectangular, and a =6 b.
(answer: µs > b/a)

Homework Equations


Ff = μ x Fn
F = ma

The Attempt at a Solution


What are the conditions in which the box may tip over? I get what the question is asking of me but I don't really understand how I should first approach it.
 
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hi morrisj753! :smile:
morrisj753 said:
What are the conditions in which the box may tip over?

the box will tip if the vertical line through its centre of mass does not go through its area of contact with the surface :wink:
 
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