Two blocks of masses m and 2m are connected by a spring of force constant k on a smooth horizontal surface. The spring is initially compressed by x₀ and both blocks are released from rest. When the spring first reaches its natural length, the speed of the block of mass m is:
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Question

Two blocks of masses m and 2m are connected by a spring of force constant k on a smooth horizontal surface. The spring is initially compressed by x₀ and both blocks are released from rest. When the spring first reaches its natural length, the speed of the block of mass m is:

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G1 Physics · Accepted Answer

Horizontal momentum remains zero: mv₁ = 2mv₂, so v₁=2v₂. Energy conservation at the natural length gives ½kx₀² = ½mv₁² + ½(2m)v₂². Substituting v₁=2v₂: ½kx₀² = 3mv₂². Hence v₂=x₀√[k/(6m)] and v₁=2v₂=x₀√[2k/(3m)].