G-Forces in a Looping Water Slide

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Since I am looking for the speed after it goes a certain distance, the best bet is to use the Work-Energy principle. If I take the person plus the Earth as the system, then I will still have the frictional force doing work as it slides down. Let me call the length of the slide s. This makes the work-energy principle like this:

In order to find the speed at the bottom, I will need to first find a value for the frictional force. Looking back at the force diagram, the forces in the direction perpendicular to the slide must add up to zero since the person doesn’t accelerate that way. Along with this, I can use the model for friction that says it is proportional to the normal force.  more...