What is the minimum speed the car must have at the top?

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Homework Help Overview

The problem involves a roller coaster loop with a radius of 12m, focusing on determining the minimum speed required at the top of the loop to prevent passengers from falling out. The context is centered around concepts of centripetal acceleration and gravitational forces.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between centripetal acceleration and gravitational force, questioning why the minimum centripetal acceleration must equal gravitational acceleration to keep passengers from falling. There is also exploration of the implications of this condition, including the concept of weightlessness at the top of the loop.

Discussion Status

The discussion is active, with participants clarifying their understanding of the forces at play and how they relate to the problem. Some have provided explanations regarding the conditions under which passengers remain in their seats, while others are still grappling with the concepts involved.

Contextual Notes

Participants are navigating assumptions about the definitions of "falling" and "weightlessness" in the context of the roller coaster scenario. There is a noted lack of consensus on the interpretation of these terms, which may affect their understanding of the problem.

Epsillon
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Homework Statement



A roller coaster loop has a radius of 12m. If the passengers in a car are not to fall out at the top of the loop, what is the minimum speed the car must have at the top?


The Attempt at a Solution


Alright I think I got the right answer but I do not completely understand the question.

so what i did was

I went Fc=Fg (but why??)

g is 9.8
mg=mv^2/r

g=v^2/r
v=11

But I don't get why the MINIMUM ac has to be g for them not to fall off.
 
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Epsillon said:
But I don't get why the MINIMUM ac has to be g for them not to fall off.


If the acceleration is less than g, then the force on passengers due to the acceleration of the roller coaster will be less than that on the passengers due to gravity and gravity will "win", i.e. the passengers will fall.

Therefore, if the minimum acceleration is equal to g the force will allow for passengers to remain in their cars (i.e. the force due to gravity won't be able to "overcome" the force due to the centripetal acceleration) and an acceleration greater than g will obviously have the same effect.

I hope this makes sense to you. I'm not that hot at explaining, so perhaps someone else can put it better?
 
OHHH so this questions is defining falling as the car not going around the cirlcle.

I thaought it means that they go weightless.
 
Epsillon said:
OHHH so this questions is defining falling as the car not going around the cirlcle.

I thaought it means that they go weightless.

Think about what you said...remember that Weight = Mass x Gravitational Acceleration (g) so, when the centripetal acceleration of the car equals g, the passengers subject to this force (due to the centripetal acceleration) are in effect "weightless", which is why they don't fall (the force due to the centripetal acceleration cancels the force due to gravity).

I can't get latex to work, but the vectors, for this case is:

Weight = mass x (centripetal acceleration + gravitational acceleration)

at the top of the loop this means that, with centripetal acceleration = g and g and centripetal acceleration directed opposite each other

Weight = mass x 0 = 0

Make sense?
 

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