The 8-lb block slides in a frictionless slot that lies in the vertical plane. The stiffness’s of springs A and B attached to the block are kA =40 lb/ft and kB= 20 lb/ft. When the block is in position 1, spring A is compressed 0.5 ft and spring B is unreformed. If the block is launched in position 1 with the speed v1 down the slot, find the smallest v1 that will enable the block to reach position 2.
(Hint: the kinetic energy (T) at point 2 should be 0)