Two blocks of mass 3 kg and 6 kg lie on a smooth horizontal surface, joined by a light spring of force constant k = 200 N/m that is initially unstretched. The blocks are given velocities (as shown) such that they approach each other with a relative speed of 3 m/s along the line of the spri

Question

Two blocks of mass 3 kg and 6 kg lie on a smooth horizontal surface, joined by a light spring of force constant k = 200 N/m that is initially unstretched. The blocks are given velocities (as shown) such that they approach each other with a relative speed of 3 m/s along the line of the spring. Find the maximum extension (or compression) of the spring.

Accepted Answer

30 cm. At maximum extension the relative velocity is zero, so the kinetic energy of relative motion converts to spring PE: (1/2)*mu*v_rel² = (1/2)*k*x² with mu = 2 kg and v_rel = 3 m/s gives x = 0.30 m = 30 cm.

Solution

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