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 1.66 kg and Block B has mass 3.28 kg. On the left side, Spring 1 has spring constant 2,645 N/m and on the right side, Spring 2 has spring constant 5,412 N/m. Block A compresses Spring 1 by 4.73 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? Write your answer with three significant figures and write the answer in centimeters (cm).

Explanation / Answer

Initial kinetic energy of block 1=0.5kx2=0.5*2645*0.04732=2.9588J

velocity of block=sqrt(2K/m)=1.888m/s

Velocity of system after collision=m1v1/(m1+m2)=0.6345m/s

Kinetic energy of system=0.9943J

Compression in spring 2=sqrt(2K/k)=1.92cm

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