Two uniform disks with the same mass are connected by a light inextensible string supported by a massless pulley on a frictionless axis. the string is attached to a point on the circumference of disk a (on the left) and is wound around disk b (on the right) so that the disk will rotate like a yo-yo when dropped.

Aspring is used to stop a 50-kg package which is moving down a 20º incline. the spring has a constant k = 30 kn/m and is held by cables so that it is initially compressed 50 mm. knowing that the velocity of the package is 2 m/s when it is 8 m from the spring and neglecting friction, determine the maximum additional deformation of the spring in bringing the package to rest.