# Need help with a physics problem

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.

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NateTG
Homework Helper
According to the illustration, the highest point that the roller coaster reaches is at the other end. So, if energy is conserved, you have the minimum kinetic energy at h=20. Since the starting point is h=15, there is a change in height of 5m, so KE=mgh=m50=1/2 m v2.

The initial velocity is 10 m/s.

The energy stored in a spring is 1/2 kx2 where x is the displacement of the spring. Clearly to stop the roler coaster, the spring must store all of the energy of motion of the roller coaster.

THanks...but the start is at the right side. My teacher drew it all crazy. Does that make a difference though?

Also I'm not sure if it's clear but the problem is saying that the train starts from the right with initial velocity, v, goes through to the left bounces off the spring and returns to the initial point (on the right). So the minimum initial velocity is to go from right to left to right? Hopefully that makes more sense.

Anyone else?