posted by carlton .
A 20.0 kg block is connected to a 30.0 kg block by a string that passes over a light, frictionless pulley. The 30.0 kg block is connected to a spring that has negligible mass and a force constant of 300 N/m, as shown in the figure below. The spring is unstretched when the system is as shown in the figure, and the incline is frictionless. The 20.0 kg block is pulled 20.0 cm down the incline (so that the 30.0 kg block is 40.0 cm above the floor) and released from rest. Find the speed of each block when the 30.0 kg block is 20.0 cm above the floor (that is, when the spring is unstretched).
The spring is also causing the blocks to move in same direction as the Net force:
Workspring = ½ k xi2 - ½ k xf2
Workspring = ½ 250 0.22 - ½ 250 02
Workspring = 5 J
Workgravity + Workgspring = ½ m v2
33.6 + 5 = ½ (20+30) v2
v = 1.25 m/s