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## Homework Statement

A mass of 122 g is attached to a vertically hung spring. The mass stretches the spring 13.8 cm. (a) What is the spring constant of the spring? (b) If the mass is dropped from rest from a position where the spring is just relaxed, what will be the maximum distance the mass will stretch the spring?

## Homework Equations

W = ΔK + ΔP

Gravitational P.E = mgh

Spring P.E = 1/2kx²

## The Attempt at a Solution

(a) What is the spring constant of the spring?

I used a FBD to see that the only relevant force working here would be the force of gravity....so mg.

spring constant = Force / Δx

We're given Δx = .138m

Force would be just the mg I believe...so if that is true

K = F / Δx = 1.1956 / .138 = 8.66 for the spring constant

(b) If the mass is dropped from rest from a position where the spring is just relaxed, what will be the maximum distance the mass will stretch the spring?

For here I'm not too sure....I tried using Work = Δk + ΔP

so I did

mgh (also written as mgΔy) for the gravitational potential energy + 1/2Kx² for the spring potential energy, and since velocity would be 0 the kinetic energy wouldn't apply

so

mgΔy = 1/2Kx²

I'm not sure if this is the right way to be approaching this...

any hints here?