Roller coaster circular motion normal forces

AI Thread Summary
At the top of a circular hill with a radius of 17 m, a roller-coaster car with a mass of 1200 kg experiences different normal forces depending on its speed. For a speed of 8.2 m/s, the calculated normal force is approximately -4746.35 N, while at 17 m/s, it is about -20,400 N. The forces acting on the car include the weight and the normal reaction, which together provide the necessary centripetal force to maintain the car's motion. The discussion highlights confusion regarding the correctness of these calculations and seeks clarification on the approach. Understanding the balance of forces is crucial for accurately determining the normal force in circular motion scenarios.
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Homework Statement


A roller-coaster car has a mass of 1200 kg when fully loaded with passengers. As the car passes over the top of a circular hill of radius 17 m, its speed is not changing. (a) At the top of the hill, what is the normal force (using the negative sign for the downward direction) FN on the car from the track if the car's speed is v = 8.2 m/s? (b) What is FN if v = 17 m/s?

Homework Equations


-Fn= m (-v^2 / R)

The Attempt at a Solution



A) 1200(- 8.2^2/ 17)
-Fn= -4746.352941

B) 1200(- 17^2/ 17)
-Fn= -20,400 N
do not believe these answers are correct, but cannt determine any other way to solve, thanks for the help
 
Last edited:
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Consider the forces acting on the car at the top of the loop. The normal reaction,R, upwards and the weight,W. The resultant of theses 2 provide the centripetal force needed to keep the car on the track. So that resultant force=Weight-Normal Reaction.
 
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