Calculating a force constant using kinetic and potential energy?

[erik-the-red]

You are designing a delivery ramp for crates containing exercise equipment. The crates weighing 1500 N will move at a speed of 2.00 m/s at the top of a ramp that slopes downward at an angle 24.0^\circ. The ramp exerts a kinetic friction force of 540 Non each crate, and the maximum static friction force also has this value. Each crate will compress a spring at the bottom of the ramp and will come to rest after traveling a total distance of 7.90 m along the ramp. Once stopped, a crate must not rebound back up the ramp.

Question:

Calculate the force constant of the spring that will be needed in order to meet the design criteria.

My answer is 27.4 N/m, but I am not quite sure that it is correct.

I know K_1=(1/2)(1500/9.80)(2.00^2)=306 J

K_2 is zero. U_1 is also zero. W_f is -4270 J. I define x_2=7.90m.

So, I should use the equation K_1+U_1+W_f=mgy_2+(1/2)(k)(x_2)^2.

y_2=x_2*sin(24.0^\circ)=3.21. But, it is -3.21 because y_2 is below y_1=0.

Using the equation I believe I should use, I got the answer to be k=27.4 m/s.