How Far Does the Block Compress the Spring?

[MUFfL3r]

Homework Statement

A block with a mass of 1.40 kg is free to slide down a plane inclined at an angle of 20° above horizontal (the block will slide down and to the left). Before it is released from rest, it is a distance of d = 2.30 meters away from the end of a spring with spring constant 400 N/m. Assume there is no friction. g = 9.80 m/s²

mass = 1.40 kg
ϴ = 20°
d = 2.30 m
k = 400 N/m
g = 9.80 m/s²a) When the the compression of the spring is a maximum, what is the distance that the spring is compressed past equilibrium point?

b) When the block is on the way back up the ramp, how fast is it going at the moment it loses contact with the spring?

Homework Equations

Conservation of energy:
PE = 1/2kx²
PE = mgh

The Attempt at a Solution

a) I worked it out to mgd(sinϴ) = -mgd(sinϴ) + ½kx² is that right?

b)Well I know I need to find velocity. But I'm having a hard time trying to figure out how I would relate the equations together. Any helpful hints?

 

[ehild]

Draw a picture and show both the initial and the final positions of the block, when the spring is compressed and the block stopped.

ehild

 

[Lame One]

A bit of a hint for the velocity: If there is no friction, then energy is going to be in either the block or the spring at any given time.