Calculating Rollercoaster Energy and Designing for Conservation

[BlueCardBird]

Homework Statement

So there's an assignment that I must complete which is to build a rollercoaster. The main problem is during the blueprint stage, I'm extremely confused with the calculations. This roller coaster must have one loop, a collision and 2 hills, the goal is the conserve the most energy as a object (marble) going through the circuit. In addition the rollercoaster must be activated by a spring. What I had in mind was to have one hill, a collision followed by another hill and finally the loop. Further more, the height of the first hill may be at most 30.cm above the finishing height. The starting height may be up to 15 cm above the bottom.

Homework Equations

Ek=1/2mv^2
Eg=mgh
Fc=m(v^2/r)
Es=1/2kx^2

The Attempt at a Solution

To be honest I just need to find a radius of the loop and k value for the spring but I have no idea where to start calculation, it seems like always one variable is missing. Can anyone give me a start?

 

[haruspex]

What you need from the spring is energy, so it could be a high k or a long displacement.
What springs are available?
Need more info re the collision. Are there two marbles, the first impeling a second, and only the second making it to the end? If not, what is the collision?
For the loop, there is a minimum speed to ensure it stays in contact all the way round. Do you know how to calculate that?

 

[BlueCardBird]

Well for the collision the second marble must finish the track keep in mind that the goal is to have the most mechanical energy conserved from beginning to end. The compression of the spring and constant are decided by me but i don't have enough information to calculate it i don't know whether i should set a radius and calculate the rest from there or to find a spring and calculate the radius that way.

 

[haruspex]

So how would you arrange the collision so as to minimise loss of energy?
If you can find a spring to meet whatever requirement, you could start from the end and work backwards. You didn not answer my question about making it around the loop.

 

[BlueCardBird]

The spring has no requirements and as for the loop I am not aware of that, to my knowledge its just Fc=m(v^2/r) and you can find the radius that way.

 

[haruspex]

as for the loop I am not aware of that, to my knowledge its just Fc=m(v^2/r) and you can find the radius that way.

So the minimum speed at top of loop is?