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 4.46 kg and Block B has mass 2.13 kg. On the left side, Spring 1 has spring constant 5,896 N/m and on the right side, Spring 2 has spring constant 3,978 N/m. Block A compresses Spring 1 by 4.9 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

Speed of block A before collision=v 0.5kx2=0.5mv2 v=4.247m/s Velocity after collision=u By momentum conservation, 4.247*1.68=(1.68+1.72)u u=2.098m/s Conserving energy upon collision with spring, 0.5*(1.68+1.72)*2.0982=0.5*2171*x2 Solving for x, x=8.30cm

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