Ok so here's the picture that the problems are based on. Background Info: The amusement park decides to redesign the rollercoaster by removing the safety ramp and replacing it with an ideal spring that will shoot the cart back through the roller-coaster backwards. The stretch of frictional track is made frictionless, set to 10.0 m long, and the giant spring is set up as shown, over another frictionless stretch of track. As a note, the ramp on the far right is not part of the track. Also this is assuming that gravity is 10 m/s^2. Question 1: What minimum initial velocity does the car nee dto make it back to the top at the start of the ride? I know this had to do with conservation of energy but I don't have any velocities to start off with, so I can't do any kinetic energy calculations. Question 2: If the park only has 20.0 m of space to devote to the slowing of the cart by the spring, what is the "k" of the spring required to get the cart to slow to a stop? Again I am completely lost as to what to do here. Any help would be greatly appreciated. I don't want to fail. :( EDIT: D'oh. Didn't see the homework help zone. Sorrow.