A uniform rectangular block ( dimentions are LxWxH, with W<L<H) of mass M rests

Question

A uniform rectangular block ( dimentions are LxWxH, with W<L<H) of mass M rests on the floor with coefficient of static friction mu (u). You want to                    apply a force F horizontally on the block to push it across the floor. How high above the floor must you apply the force to make the block slide and not tip                    over? Put you answer in terms of the mass and dimensions. Assume the block is standing with its smallest face in contact with the floor, and you push on the                    largest face.

Explanation / Answer

writing the equation of forces acting on the block, we have

N=mg

uN=F

so F=umg

also let F is applieed at a height h above the floor

and mg is acting vertically downwards at a distance W/2 from the edge about which it may topple

then taking the torque of the forces about that edge, we have

Fh=mgW/2

=>h=mgW/2F

=>h=mgW/2umg

=>h=W/2u

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