Two blocks slide on a horizontal, frictionless surface with two springs on oppos

Question

Two blocks slide on a horizontal, frictionless surface with two springs on opposite sides. Block A has mass 1.65 kg and Block B has mass 2.42 kg. On the left side, Spring 1 has spring constant 2,702 N/m and on the right side, Spring 2 has spring constant 5,989 N/m. Block A compresses Spring 1 by 3.01 cm and is released from rest toward Block B and Spring 2. Block A hits Block B (which is initially at rest) and has a perfectly inelastic collision. The blocks, now stuck together, then head toward Spring 2 and compresses the spring. What is the maximum compression of Spring 2?

Explanation / Answer

1/2 2702*(0.0301)^2 =1/2 *1.65 *v^2 hence v of block A before collision =1.22 m/s also by conserving momentum 1.65*1.22 =(1.65+2.42)v hence v =0.5 m/s and by conserving energy to find max compression 1/2 (1.65+2.42)*0.5^2 =1/2 *5989 x^2 hence x =compression = 0.0129 m =1.29 cm

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