(Solved): 8. Consider the two mass system shown below. The mass \( m \) is pulled down by gravity and pulls t ...

8. Consider the two mass system shown below. The mass \( m \) is pulled down by gravity and pulls the mass \( M \) by a massless cable. The mass \( m \) starts a height \( L / 2 \) from the ground and the mass \( M \) starts a distance \( L \) from the ledge (from the COM of \( M \) ). Assuming the mass \( M \) experiences dynamic friction (with constant \( \mu_{d} \) ), derive a formula for the minimum value of \( M \) so the block does not fall off the ledge. Assume that pulley B is fixed and massless.