Solving problems usng conservation of energy

[tutojean]

Homework Statement

A block of mass 1.5 kg is placed against a horizontal spring of force constant k that is compressed .20 m. the spring is then released and the block travels to the right along a horizontal surface. The coefficient of kinetic friction between the block and the surface is 0.4. After the block has traveled 0.9 m to the right, measured from its initial position against the compressed spring, its velocity is 14.5 m/s. Calculate the force constant k of the spring.

Homework Equations

Kinetic/gravitational/elastic/friciton (Usage varies for different situations.

The Attempt at a Solution

[0+0+Es] Initial = [K+0+0+Ef]

1/2kv^(2) = 1/2mv^(2) = uNd

N=fg=mg so this replaces N essentially!

plugging in...

1/2k(0)^(2) = 1/2(1.5)(14.5)^(2) + (.4)(1.5)(9.8)(.9)

k=320.667
k=321 Nt

Is this correct? Just needing full proof assistance thank you so much.

 

[kuruman]

The method is correct but you need to redo the numbers because they don't agree with mine. What number did you put here (in red)?

1/2k(0)^(2) = 1/2(1.5)(14.5)^(2) + (.4)(1.5)(9.8)(.9)

k=320.667
k=321 Nt