Physics contest - question 2

Physics contest -- question 2

Suppose you are to move a piece of heavy furniture at home. Let us approximate it by a cubic block of unifor mass M on a rough floor surface with friction coefficient u=1. Your strength can only provide a force F=0.8Mg, where g is the gravity acceleration, so you cannot simply lift the block and move it around.

a) If you apply the force as shown in the figure, what will happen to the block?

b) You are free to apply the force F in any direction to any point of the block, how to apply the force so the block will have maximun acceleration in sliding motion but without tipping over?
(I know part b is pretty easy but I failed to answer it :frown:)

[There may be many ways and you are only required to find one. YOu many also need this : sinθ+cosθ=1.414sin(θ+45)]
[Hint: The magnitude of the friction is the smaller of the two : F or uN, where N is the reaction force of the floor perpendicular to the furface. The effect of the friction is to keep the block from sliding until it reachers its maximum value uN)

a) It will tip over. (I answered it in more detail during competition)
 

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