A 20kg block is connected to a 30kg block by a string that passesover a light fr

Question

A 20kg block is connected to a 30kg block by a string that passesover a light frictionless pulley. The 30kg block is connectedto a spring that has a negligible mass and a force constant of250N/m. The spring is unstretched when the system is as shownin the figure, and the incline is frictionless. The 20kgblock is pulled 20cm down the incline (so that the 30kg block is40cm above the floor) and released from rest. Find the speedof each block when the 30kg block is 20cm above the floor (that is,when the spring is unstretched).

Explanation / Answer

   m1 = 20 kg
   m2 = 30 kg
   k = 250 N / m
   x = 20 cm
      = 0.20 m
   x '= 20 cm
      = 0.20 m
   y = 40 cm
      = 0.40 m
   in the system the blocks start from rest so we canchoose that
   PEg = 0
   if we apply law of conservation of mechanical energyfrom the released position to the final stage
   we get    
   (KE + PEg + PEs)f =(KE + PEg + PEs)i then weget
   (1/2) (m1 + m2)vf2 + (m1 g x' sin40o - m2 g y) + 0 = 0 + 0 + (1/2) kx2
   vf = ............... m / s

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