Circular motion problem

[bloodlust_X]

Homework Statement

During the Physics Field Trip to Six Flags, Skyler and Jayson experienced a looping roller coaster ride for the first time. Their 656-kg roller coaster car was moving at 15.8 m/s at the top of the loop where occupants experienced a normal force equivalent to 1/4-th their weight. Determine the radius of curvature of the loop.

Relevant Equations

So I tried using F = mv^2/r, and f =mg to cancel mass but it didn't work, also its confusing which forces are supposed to be used?
Fnet would otherwise be 4281N, after subtracting 1/4 of rollercoaster's weight?

Could someone please help me solve this?

 

[Orodruin]

Please give us your actual attempt including the equations you wrote down. Show us what you did, don’t just describe it in words.

 

[haruspex]

occupants experienced a normal force equivalent to 1/4-th their weight.
…
after subtracting 1/4 of rollercoaster's weight

It's the occupants that you have the normal force info on. Have you drawn a Free Body Diagram for one of those? What forces does it show?

Btw, you can't actually find the radius of the loop as a track, only the radius of arc the occupant's mass centre is following.

 

[bloodlust_X]

Please give us your actual attempt including the equations you wrote down. Show us what you did, don’t just describe it in words.

 

[bloodlust_X]

It's the occupants that you have the normal force info on. Have you drawn a Free Body Diagram for one of those? What forces does it show?

Btw, you can't actually find the radius of the loop as a track, only the radius of arc the occupant's mass centre is following.

so nothing to do with the mass of the rollercoaster in the problem?

 

[Orodruin]

That doesn’t really tell us what you did. Please type it out with your arguments in between the equations. (See the homework guidelines)

 

[haruspex]

As @Orodruin notes, posting that working doesn't tell us what principles you are using. But reverse engineering your first equation, it says centripetal force = gravitational force/4. Is that what the question says?