Work-Energy: Finding Contact Force at Lowest Point

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To find the contact force at the lowest point of a skater sliding down a parabolic track, one must first determine the minimum of the quadratic equation y = (12/121)x^2, which represents the track's height. At this minimum, the skater's motion is horizontal, indicating that gravitational force and the normal force are the primary forces at play. The gravitational force acting on the skater is equal to their weight, while the normal force counteracts this weight at the lowest point. The absence of friction simplifies the analysis, focusing solely on these two forces. Understanding these dynamics is crucial for accurately calculating the contact force.
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Homework Statement



Suppose a skater is sliding down a parabolic track of known height of 12 meters. You are also given the quadratic equation of the track in terms of x and y, which are in meters. Neglecting friction, how would you find the contact force between his wheels and the track at the lowest point (the minimum of the quadratic equation)?

Homework Equations



y = (12/121) x^2

The Attempt at a Solution



I'm not sure how to attack this problem. Any help would be greatly appreciated!
 
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At the lowest quadratic minimum, the motion is purely horizontal.
What force(s) are involved?
It appears to me to be a very simple problem with only one force . . .
 
Yeah, it seemed too simple to be correct...
 

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