Homework H$\mathrm{.}4.$N

Given: Blocks A and C $($having masses $\backslash ($ m $\backslash )$ and $\backslash (2$ m $\backslash ),$ respectively$)$ are connected by an inextensible cable. This cable has been fed through a third block B $($having a mass of $\backslash (2$ m $\backslash )),$ as shown in the figure below. The system is released from rest with A being located at a distance of D below B$.$ In the subsequent motion, block A contacts block B and sticks after a short time $\backslash (\backslash$Delta t $\backslash )$ following their initial contact. Assume that the cable does not break and that the mass of the two pulleys is negligible.

Find: For this problem:

$($a$)$ Determine the maximum height attained by block B after its contact with and sticking to block A$.$

$($b$)$ Determine the average tension force in the cable during the during of the impact time $\backslash (\backslash$Delta t $\backslash )$ between A and B $.$