Solving for Distance: Finding Work from Mass, Incline & Spring

[UrbanXrisis]

there's a 3kg mass on a 30 degree frictionless incline. The mass travels d distance and hits a spring with k=400N/m. The spring contracts 0.2 m and brings the block to a stop.

I need to find the distance the block traveled.

F=kx
F=400*.2
F=80N

so the block has to hit with 80N.
what formula would I use to get distance? I am confused because if I used any energy formula (which I know I will have to) the question is in Joules instead of Newtons. What should I do?

 

[Skomatth]

You can solve this with energy.
At any point on the block's path you can find its energy with the equation
$$E = .5kx^2 + .5mv^2 + mgy$$

Consider when the spring has been fully compressed to be y=0. Can you do it from there? Note: y does not equal d.

 

[UrbanXrisis]

are you saying that:
E=80N+.5mv^2 ?

 

[delton]

Heres the easiest way to solve the problem:
We know the spring compressed .2 meters. How much energy did the block impart to the spring to do this? We can find out using the potential energy of a spring formula $$E = .5kx^2$$ Under the conservation of energy, the potential energy of the block at the top of the ramp must be equal to the PE of the spring. Use $$E = mgy$$ to find y and then use trigonometry to find the hypotonuese of the triangle.
Remember : the key to sucsess in physics is thinking; not memorizing how to do every possible problem.