Hi, I'm a student at the University of Pennsylvania, and these two
problems have been confusing me - any help would be greatly
appreciated!


1. Two planks, each of mass m = 1.4 kg and length L = 0.6 m are
connected by a frictionless, massless hinge as shown in the figure
above. Initially the system is at rest on a level, frictionless
surface. The vertical plank falls counterclockwise and finally comes
to rest on top of the horizontal plank. Find the displacement and the
linear speed of the hinge just after the the two planks come into
contact.





2. An Atwood's machine consists of a hollow, thin-walled cylinder
(mass M and radius R) which can rotate frictionlessly about an axis
through its center, a massless and stretchless rope, and two masses,
m1 and m2. If m1 and m2 are initially held at rest and then released,
find the acceleration (direction and magnitude) of m2 and the tension
in the string attached to it immediately after release. Assume that m1

m2 and that the rope moves without slipping along the cylinder. Your

answers should make use ONLY of the assumed known quantities such as
m1, m2, g, M, or R.