Distance a spring has been compressed

[Joe_I_Am]

Homework Statement

.

A 20 kg mass, released from rest, slides 12 meters down a frictionless plane inclined at an angle of 30º with the horizontal and strikes a spring of spring constant K = 200 Newtons/meter as shown in the diagram above. Assume that the spring is ideal, that the mass of the spring is negligible, and that mechanical energy is conserved. Use g = 10 m/s², (sin30º = ½, cos 30º = 0.866)
a. Determine the speed of the block just before it hits the spring.


b. Determine the distance the spring has been compressed when the block comes to rest.


c. Is the speed of the block a maximum at the instant the block strikes the spring? Justify your answer.

Homework Equations

(1/2)kx^2, (i/2)mv^2

The Attempt at a Solution

For part b, wouldn't I just have to solve

original energy 20*10*12sin(30)= (1/2)(200)x^2

for x?

I do this and I get ~3.46 meters for x, but I'm being told that this is not the right answer.

What am I doing wrong? If energy is conserved, then (1/2)kx^2 would have to equal the original mgh

 

[Doc Al]

What am I doing wrong? If energy is conserved, then (1/2)kx^2 would have to equal the original mgh

Don't neglect the additional change in height as the spring is compressed. (Measure h from the lowest point, not the point where the mass first touches the uncompressed spring.)