A block of wood 10cm by 10cm by 40cm with mass 3.2kg and uniformdensity stands on its end on level ground. In the following, assume that static friction with the ground is large enough that if I push on the block, it does notslide.
a) Imagine that I slowly push the block from the left so that ittilts by rotating about the lower right edge. At some point the block tips over and falls tothe ground without any further pushing required. Where is the center of mass of the blockwhen that happens?
b) How much work is required to get the block to the“tipping point” in part (a)?
c) Now, suppose I were to shove the block, give it a quick push sothat it starts rotating about the lower right edge. How much angular momentum must theshove impart to the block so that it rotates up to the tipping point (Hint: how muchrotational kinetic energy must it have to make it to the tipping point)?
d) A 1.00g bullet is to be fired horizontally (in a directionparallel to one of the 10cm edges) into the center of the block. Assuming the bullet embeds inthe wood, how fast must it be going to knock the block over if static friction islarge enough that the block does not slide along the ground when struck?
(Hint: I suggest youanswer the following questions about the bullet/block interaction before proceeding: Is mechanical energy conserved in this process? Is the angular momentum about the lowerright edge of the block conserved? What is the initial angular momentum of thebullet?)