Rollercoasters and Loops and Normal Forces

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SUMMARY

The discussion focuses on calculating the normal force at the top of a loop in a rollercoaster scenario using the variables mass (m), gravitational acceleration (g), and radius (r). The initial equation derived is FN = mV²/r - mg, indicating that the normal force (FN) is dependent on the centripetal force (Fc) and gravitational force (Fg). A participant suggests that the solution should account for the minimum height required for the rollercoaster to maintain motion through the loop, prompting a need for a more general equation for FN applicable at any height.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with centripetal force concepts
  • Basic knowledge of gravitational force equations
  • Experience with algebraic manipulation of equations
NEXT STEPS
  • Research the derivation of centripetal force equations in circular motion
  • Study the concept of minimum height for loops in rollercoaster physics
  • Explore the relationship between velocity, radius, and gravitational force in loop dynamics
  • Learn about energy conservation principles in rollercoaster design
USEFUL FOR

Students in physics courses, particularly those studying mechanics, as well as educators and anyone interested in the physics of rollercoasters and circular motion dynamics.

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Homework Statement


<I will attach a diagram below> In terms of m, g and r. FInd the normal force at the top of the loop.

Homework Equations


∑F = Fc = FN+Fg ∴ Fc=FN+Fg ∴FN = Fc - Fg ∴ N=mV2/r - mg

The Attempt at a Solution


Fc=mV2/r - mg and V2=ra and a=g ∴C=mrg/r ∴C = mg ∴mg-mg=N ∴ N=0 N. BUT after discussing with a guy in AP Physics C at my school, he said that this is solving for the minimum height. SO I think I need to solve for the general equation to solve for the normal force at the top of the loop at any height using the variables m, g, and r only (I'm pretty sure that's what my instructions meant). Could anyone help please? I will send an image of my work as well.
 
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