Solving for Spring Compression: 2.3kg Dropped 4.82m

jamexd
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Homework Statement


A mass of 2.3 kg is dropped from a height of 4.82 meters above a vertical spring anchored at its lower end to the floor. If the spring constant is 20 N/cm, how far, to the nearest tenth of a cm, is the spring compressed?
answer is 34.1

Homework Equations


PE = mgh
KE = (1/2)m(v^2)
Hookes Law= (1/2)K(x^2)

The Attempt at a Solution


mgh = (1/2)K(x^2)
 
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There you go, that is how you solve the equation. The actual solution, however, is wrong. Did you keep your units?
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
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