A spring with spring constant \"k\" is positioned vertically and then compressed

Question

A spring with spring constant "k" is positioned vertically and then compressed from its equilibrium length by a distance "DELTAx." A block of mass "m" is placed on top of the spring, and is launched into the air when the spring is released. (This is similar to the projectile launcher you used earlier in the semester and will use in this mini-lab.) To what maximum height "hmax" will the block travel? Show how you arrived at your answer. SOLVE FOR HMAX explicitly with proof please!!

Explanation / Answer

Spring stored energy = 0.5kx^2 PE of mass at highest point Fs = mg(hmax) mg(hmax) = 0.5k(deltax^2) =>hmax = k(deltax^2)/2mg

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