How to solve for final velocity of object pushed by spring using concept of engergy

[divgrad]

Here is the given problem:

http://img213.imageshack.us/img213/6781/problemtk6.jpg

Here is my incorrect solution:

http://img152.imageshack.us/img152/6698/solutionzm3.jpg


Why should distance even matter for the final velocity in this problem since once the spring is uncompressed, the cart will continue at a steady velocity forever since there is no friction or air resistance?

The answer for (a) is 1.47 m/s, and the answer for (b) is 1.35 m/s. Again, why would the velocity be less for part (b) when there is no energy loss from either friction or air resistance?

 

[Ja4Coltrane]

Because the problem says that the glider is attatched to the spring.

 

[Doc Al]

I think you have an incorrect mental picture of the system. The glider is attached to a spring which, in turn, is fixed to some point on the track (or attached to a wall, for instance). So, once the glider passes the unstretched position, the spring starts pulling instead of pushing, thus slowing the glider.

 

[divgrad]

Ok, I was thinking the spring (which is attached to the glider) was compressed then allowed to push off of a wall and push the glider and spring backwards.