A fish scale, consisting of a spring with constant k = 150N/m and a pan to hold

Question

A fish scale, consisting of a spring with constant k = 150N/m and a pan to hold the fish, is hung vertically from the ceiling. Assume the pan has a negligible weight, so the spring is initially unstretched when a fish is placed in it. The fish/pan start from rest and fall downward until the spring is fully stretched. (They then come back up as the spring contracts, but that isn’t important for the calculations here.) If the fish has a mass of 6.0 kg, what is the maximum distance through which it falls?

Not to sure what equation I should be using

Explanation / Answer

Let ymax is the maximum distance through which it falls

Apply Conservation of energy

maximum gain in potentail energy = loss of potentail energy

(1/2)*k*ymax^2 = m*g*ymax

ymax = 2*m*g/k

= 2*6*9.8/150

= 0.784 m <<<<<<----------Answer

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