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 1.14 kg and Block B has mass 3.27 kg. On the left side, Spring 1 has spring constant 3,173 N/m and on the right side, Spring 2 has spring constant 4,817 N/m. Block A compresses Spring 1 by 3.98 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

use conservation of energy: at the beginning we have only potential energy of spring A, at the end we have potential energy of spring B. k1x1^2/2 = k2x2^2/2 k2x2^2/2=3173*(0.0398)^2/2=2.513 --> x2=0.0323 m= 3.23 cm

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