A 15.0-kg block is attached to a very light horizontal spring of force constant

Question

A 15.0-kg block is attached to a very light horizontal spring of force constant 500.0 N/m and is resting on a frictionless horizontal table. Suddenly it is struck by a 3.00-kg stone traveling horizontally at 8.00 m/s to the right, whereupon the stone rebounds at 2.00 m/s horizontally to the left.
(a) Find the maximum distance that the block will compress the spring after the collision

** Please explain concepts/ calculations used in more detail; I'd like to use this answer to study, so a lot of explination of how you got certain parts of the answer is also greatly appreciated.

Explanation / Answer

first of all conserving momentum we have the velocity of the 15 kg block 3*8 = 3*-2 +15*V => V = 2m/s to the right => now a velocity is induced to the block which gives it a kinetic energy of 1/2*15*4 = 30 J this kinetic energy is converted to potential energy stored in the spring at maximum. displacement. => 1/2*500*x^2 = 30 => x = 0.346 m =34.6 cm

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