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 1.68 kg and Block B has mass 1.72 kg. On the left side, Spring 1 has spring constant 5,128 N/m and on the right side, Spring 2 has spring constant 2,171 N/m. Block A compresses Spring 1 by 3.73 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). Do not include the units in the space below.

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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