A block of mass m is attached to a spring of force constant k along the smooth face of a freely moving wedge of mass M and angle θ. Initially the spring is unstretched and the entire system is at rest. The block is released. The maximum extension of the spring is:
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Question

A block of mass m is attached to a spring of force constant k along the smooth face of a freely moving wedge of mass M and angle θ. Initially the spring is unstretched and the entire system is at rest. The block is released. The maximum extension of the spring is:

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G1 Physics · Accepted Answer

At the initial state and at maximum extension, all velocities are zero. Therefore wedge recoil does not affect the turning-point energy balance. The block descends a vertical distance x sinθ, so mgx sinθ = ½kx². For x ≠ 0, x_max = 2mg sinθ/k.