Maximum velocity at the top of a roller coaster?

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Homework Help Overview

The problem involves determining the maximum speed of a roller-coaster car at a specific point on the track, given its mass and the radius of the circular path. The context is centered around forces acting on the car at the top of the roller coaster.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the forces acting on the roller-coaster car, particularly the normal force and gravitational force. There is an exploration of what happens to the normal force as the car approaches the point of leaving the track, leading to a calculation of maximum speed using the relationship between these forces.

Discussion Status

Participants are actively engaging with the problem, with one suggesting a method to set the normal force to zero to find the maximum speed. Another participant has calculated a potential speed and expressed that it seems reasonable, indicating a productive line of reasoning is being followed.

Contextual Notes

The discussion is based on the assumption that the roller-coaster car is at the top of a circular path, and the calculations are constrained by the parameters provided, including mass and radius. There is no indication of additional information or constraints affecting the problem.

pcandrepair
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Homework Statement



A roller-coaster car has a mass of 509 kg when fully loaded with passengers.
-The radius of the circle is 15m. (See picture below)

What is the maximum speed the vehicle can have at point B and still remain on the track?
_________m/s


Homework Equations



Sum of forces in the radial direction = -m(v^2)/R



The Attempt at a Solution


There would be a normal force pointing up and mg pointing down
 

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pcandrepair said:
There would be a normal force pointing up and mg pointing down
Right. And what will the normal force become just before the car leaves the track? Use that to calculate the maximum speed. (You already know the radius of the curve at point B.)
 
So I set the normal force equal to zero just before it would leave the track and use..

normal - mg = m(v^2)/r masses would cancel.
0 + g = (v^2)/r
gr = (v^2)
sqrt(gr) = v

when i take the sqare root of 9.8*15 I'm getting 12.1244m/s which sounds reasonable.
 
Sounds good to me.
 

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