What Speed Does the Roller Coaster Need to Maintain at the Top of a 14m Loop?

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Homework Help Overview

The problem involves a roller coaster moving at the top of a loop with a diameter of 14 meters. The context centers on determining the speed required for the coaster car when the normal force acting on it is half of its weight.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply the relationship between centripetal force and gravitational force, questioning the implications of the normal force being half of the weight. Some participants raise concerns about the calculations and the assumptions regarding the minimum speed needed for circular motion.

Discussion Status

Participants are actively discussing the calculations involved, with one suggesting a slight adjustment to the original poster's result. There is an ongoing exploration of the mathematical relationships and assumptions without reaching a definitive conclusion.

Contextual Notes

The problem is constrained by the information provided, specifically only the diameter of the loop and the relationship between the forces at the top of the loop. There is a focus on the implications of the normal force being non-zero.

yashi5166
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Homework Statement


A roller coaster is moving past the top of a loop of diameter 14m. The Normal force (directed downwards) provided by the track at the top of the loop is equal to one-half the weight of the car. What is the speed of the coaster car at this point?

Homework Equations



Only the diameter is given.

The Attempt at a Solution


Fc = Fg+Fn
→ mv2/r = mg + .5(mg)

and then minimum speed to go in a circle is sqrt(gr) but that won't work cause in order for that to happen Fn has to be 0 but here is half Fg. i believe the answer is 10.12m/s
 
Last edited:
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Your math is off a bit, and round it off to 10.1m/s
 
thanks soo much
 

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