How far has the spring been compressed?

[Ry122]

A block of mass 9.0 kg slides from rest down a frictionless incline and is stopped by a strong spring with spring constant 3.50 x 10^4 The block slides 5.00 m from the point of release to the point where it comes to rest against the spring. When the block comes to rest, how far has the spring been compressed?

My attempt:
9(9.8)sin29=42.76N

Since during the 5m of motion, energy loss is going to be equal to energy gain,
i should be able to apply this equation
1/2kx^2=fxs
x= length of movement that the spring isn't compressed during.
1/2(3.5x10^4)(5-x)^2=42.76x
this doesn't yield the correct answer as x=5.11
what am i doing wrong?

 

[LowlyPion]

This looks just like:
https://www.physicsforums.com/showthread.php?t=309014
that you posted yesterday without a spring constant?

Since you are using sin29, I'm guessing that the incline is 29°.

So to solve either of these problems, you know the total energy in the system, from gravitational potential energy.

When it stops then you know how much energy must be in the spring.

From that you can readily figure the compression of the spring.