A block of wood 10 cm by 10 cm by 40 cm with mass 3.2 kg and uniform density 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 not slide.
a) Imagine that I slowly push the block from the left so that it tilts by rotating about the lower right edge. At some point the block tips over and falls to the ground without any further pushing required. Where is the center of mass of the block when 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 so that it starts rotating about the lower right edge. How much angular momentum must the shove impart to the block so that it rotates up to the tipping point (Hint: how much rotational kinetic energy must it have to make it to the tipping point)?
d) A 1.00g bullet is to be fired horizontally (in a direction parallel to one of the 10cm edges) into the center of the block. Assuming the bullet embeds in the wood, how fast must it be going to knock the block over if static friction is large enough that the block does not slide along the ground when struck? (Hint: I suggest you answer the following questions about the bullet/block interaction before proceeding: Is mechanical energy conserved in this process? Is the angular momentum about the lower right edge of the block conserved? What is the initial angular momentum of the bullet?)