Mass sliding down incline with spring

[fireearthair8]

Homework Statement

A 3kg mass starts at rest and slides a distance d down a smooth 30deg incline, where it contacts an unstressed spring. It slides an additional 0.2 m as it is brought momentarily to rest by compressing the spring (k=400N/m)

What is the initial separation d between the mass and the spring?

Homework Equations

F=ma
Vf = Vi + at
Us = 1/2kx^2
Ug = mgh
K = 1/2mv^2

The Attempt at a Solution

I'm not sure how to approach this problem yet. I know that you need to find the Vf, using mgsin30 as the acceleration and Vi=0.

 

[alphysicist]

Hi fireearthair8,

They give you Vf in the problem statement (the final velocity of that part of the motion they are referring to). What is it? Now that you also know the final speed, does that help you know what approach to use?

 

[tiny-tim]

Welcome to PF!

F=ma
Vf = Vi + at
Us = 1/2kx^2
Ug = mgh
K = 1/2mv^2

Hi fireearthair8! Welcome to PF!

Hint: forget F = ma and Vf = Vi + at.

You can do this just using energy (and d = h cos theta).

 

[Texag]

another hint:

find the work done by the spring, then compare that to the work done by gravity, which acts along the distance traveled without before touching the spring as well as the .2 m after it comes in contact with the spring.