Question
Two blocks of masses 2 kg and 4 kg are connected by a
light spring (k = 300 N/m) and placed on a smooth horizontal surface. The spring is compressed by 10 cm and released. Find the maximum speed of the 4 kg block.Solution
Let m₁ =2kg and m₂ =4kg be the masses of the two blocks. The spring constant is k=300N/m. The spring is initially compressed by x=10cm=0.1m. The initial state is when the blocks are at rest and the spring is compressed. The total momentum is zero. When the spring is released, the blocks will move in opposite directions. Let v₁ and v₂ be the velocities of m1 and m2respectively. By conservation of momentum: m₁ v₁ + m₂ v₂ = 0 2v ₁ + 4v ₂ = 0 v₁ = -2v ₂ The initial potential energy stored in the compressed spring is converted into the kinetic energy of the two blocks. By conservation of energy: 
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