Spring compression problem

Question

A block of mass $m = 1.5$kg is dropped from height $h = 85$cm onto a spring of spring constant $k=1910$N/m. Find the maximum distance the spring is compressed.

This is what I did:

$$19.1 + (\sqrt{ 19.1 ^2 + 2(19.1)(0.85)(1910)} ) / 1910$$

Yet it's wrong. What's the issue?

Answer 1

Try that. You have that $m = 1,5$kg, $h = 0,85$m and $k = 1910$N/m. Then use that you must have conservation of energy.

$$E_i = E_f$$

$$mg(h + \delta x) = \frac{1}{2}k(\delta x)^2 \implies \delta x^2 - A\delta x - Ah$$

For $A := 2mg/k = 0,015706$ such that $\Delta = 0,05464707$ and $\sqrt{\Delta} = 0,231618$ then you will have that the maximum displacement will be

$$\delta x^{max} = 0,12366$$

Try that value