This is a conservation of mechanical energy question from my phsyics class that

Question

This is a conservation of mechanical energy question from my phsyics class that my professor worked out in his powerpoint. I would appreciate if you could fully work out and explain the reasoning for the steps so I could understand the example since when I was working on it myself I got confused.

Problem Solving Using Conservation of l Mechanical Energy Example Two kinds of potential energy. A ball of mass m 2.60 kg, vertical distance 55.0 cm before striking a vertical coiled spring, which it c 15.0 cm. Determine the spring stiffness constant the spring. Assume the spring has negligible mass resistance. Measure distances from the point Where the ball first touches the uncompressed spring (y 0 at Problem Solving Using Conservation of Mechanical Energy Solution Two kinds of potential energy. AKE-AU k 590 N/m Problem Solving Using Conservation of Mechanical Energy Solution Two kinds of potential energy. U1-mgh U AK AU 0 --(U2-U1)--U2 U1 k -1590 N/m

Explanation / Answer

The total potential energy loss of the ball is m*g*h, where h is the distance it falls. If the spring deflects x m, then the energy loss is
2.6*9.8*(0.55 + 15)
The energy stored in the spring at compression x is

½*k*x² = 0.5k*x²

equate these:
2.6*9.81*(0.55 + 0.15) = 0.5k*0.15²
or, k = 1587.04 N/m

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