QUESTION:
A 200 N/m, 5 m spring on a 20 degree incline is compressed 2.3 m and a 5 kg block is placed on it. If we neglect friction, how far up the incline will the block travel? How fast will it be traveling when it is 0.2 m up the incline?
EQUATION:
1/2kx^2 + mgh + 1/2mv^2 = constant
WHAT I'VE DONE SO FAR:
Since there's initially only spring and potential energy, I solved for the initial amount of energy in the block, which would remain constant as it went up and then back down the ramp. I used 1/2kx^2 + mgh and got 574.25 J. Since that's the same amount of energy that the block will have when it's at its maximum point on the ramp (when there's only PE), I set mgh equal to 574.25 and found the height from the ground to be 11.72 m. To find the height up the ramp, rather than off the ground, I divided 11.72 by sin(20) and got 34.27 m up the ramp.
WHAT I'M CONFUSED ABOUT:
I'm not sure if I did everything correctly up to this point (particularly the height values) and I'm not sure how to solve for the velocity when the block is 0.2 meters up the ramp (isn't it already 2.7 meters up the ramp to begin with?), so I'd appreciate any help. Thanks!