Colliding blocks attached to a spring - How is the spring compressed

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SUMMARY

The problem involves two blocks, m1 = 2.4 kg and m2 = 4.6 kg, colliding inelastically, with a spring of spring constant k = 1160 N/m attached to m2. The initial velocities are 10 m/s for m1 and 2.8 m/s for m2. The correct approach to find the maximum compression of the spring involves calculating the final velocity of the combined mass after the collision and equating kinetic energy to potential energy stored in the spring. The maximum compression is determined to be 0.409 m, but this value is incorrect as the blocks momentarily come to rest at maximum compression, indicating a need to re-evaluate the energy equations used.

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"A block of mass m1 = 2.4 kg slides along a frictionless table with a speed of 10 m/s. Directly in front of it, and moving in the same direction, is a block of mass m2 = 4.6 kg moving at 2.8 m/s. A massless spring with spring constant k = 1160 N/m is attached to the near side of m2, as shown in Fig. 10-35. When the blocks collide, what is the maximum compression of the spring? (Hint: At the moment of maximum compression of the spring, the two blocks move as one. Find the velocity by noting that the collision is completely inelastic to this point.)"

I cannot seem to get this answer right.

here is how I approached the problem:

using the inelastic momentum formula:

m1v1 + m2v2 = (m1+m2) * vfinal
(2.4 * 10) + (4.6 * 2.8) = (2.4 + 4.6)*v

solving for V... i get about 5.269 m/s (this is the velocity of the system)

THEN, in order to find the amount of compression, i use kinetic energy and potential energy in a spring:

.5kx^2 = .5mv^2
.5 * 1160 * x^2 = .5 * (2.4 + 4.6) * (5.269)^2

Solving for x... i get 0.409 m.

Unfortunately, this is wrong. Any help on solving this problem would be much appreciated.
 
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when the spring compression is at a maximum, the blocks are at a turning point in the motion, v = 0
/s
 

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