Solving for Speed on a Roller Coaster's Top of Hill

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Homework Help Overview

The problem involves a roller coaster car moving over the top of a circular rise with a radius of 18 meters. The scenario describes the passengers feeling lighter, with an apparent weight of only 60% of their true weight, prompting a question about the speed of the coaster at that point.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between apparent weight and centripetal force, with some attempting to apply Newton's laws to derive the speed. Questions arise about the correct interpretation of forces at the top of the hill and the necessity of drawing a diagram to visualize the forces involved.

Discussion Status

The discussion has seen various attempts to clarify the problem, with some participants providing guidance on applying Newton's second law for circular motion. There is an acknowledgment of a misunderstanding regarding the forces involved, and one participant indicates they have resolved their confusion regarding the calculations.

Contextual Notes

Participants note that the problem is situated within an introductory physics context, and there is a suggestion to focus on the net forces acting on the passengers at the top of the hill. Some participants express uncertainty about the calculations and the setup of the problem.

SilverAu
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Homework Statement


A roller coaster car is going over the top of a 18-m- radius circular rise. At the top of the hill, the passengers "feel light," with an apparent weight only 60% of their true weight. How fast is the coaster moving?

Homework Equations


I think F=mv^2/ (r)
F=ma

The Attempt at a Solution


Attempt:
F=mv^2/r
(.6)g=v^2/r
(9.8*.6)r=v^2
5.88*18=v^2
v=10.3 m/s My answer is said to be wrong
 
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This is not advanced physics, so moving to the intro physics section.
 
SilverAu said:

Homework Statement


A roller coaster car is going over the top of a 18-m- radius circular rise. At the top of the hill, the passengers "feel light," with an apparent weight only 60% of their true weight. How fast is the coaster moving?

Homework Equations


I think F=mv^2/ (r)
F=ma

The Attempt at a Solution


Attempt:
F=mv^2/r
(.6)g=v^2/r
(9.8*.6)r=v^2
5.88*18=v^2
v=10.3 m/s My answer is said to be wrong
You did not calculate what the question asks.
It's not the centripetal force which is 60% of the weight.
Draw a diagram with all the forces.
 
OK well if I am solving for the velocity of the moving coaster, how would I do that because I've drawn the diagram with forces and I don't see it.
 
Write Newton's second law for circular motion. The acceleration is the centripetal acceleration.
What is the expression for the net force at the top of the hill?
 
If they only felt 0.6 of their weight then the centripetal force on them is 1- 0,6= 0.4 of their weight.
 
Yeah I actually just figured it out, that is the only thing I messed up... Should be
F=mv^2/r
(.4)g=v^2/r
(9.8*.4)r=v^2
3.92*18=v^2
v=8.4m/s
Thanks for helping you guys
 

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