Rollercoaster Physics: Minimizing h for a Safe Loop-the-Loop Ride

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Homework Help Overview

The discussion revolves around a physics problem related to rollercoaster dynamics, specifically focusing on determining the minimum height required for a car to successfully navigate a loop-the-loop without falling off at the top. The subject area includes concepts of potential energy, kinetic energy, and forces acting on the car during its motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants explore the conditions under which the car would fall off at the top of the loop, discussing the forces involved and the importance of a Free-Body Diagram. There are attempts to relate potential energy and kinetic energy to find the necessary speed at the top of the loop.

Discussion Status

The discussion is active, with participants engaging in clarifying the problem and exploring different approaches. Some guidance has been offered regarding the relationship between potential and kinetic energy, and the need to analyze forces at the top of the loop. Multiple interpretations of the problem are being explored, particularly concerning the forces acting on the car.

Contextual Notes

Participants mention that they have just started learning about potential energy and kinetic energy, indicating a possible limitation in their understanding of these concepts as they relate to the problem.

ledhead86
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Riding a Loop-the-loop. A car in an amusement park ride rolls without friction around the track shown in the figure. It starts from rest at point A at a height h above the bottom of the loop. Treat the car as a particle.

http://community.webshots.com/user/mmaddoxwku"

What is the minimum value of h (in terms of R) such that the car moves around the loop without falling off at the top (point B)?

I have no clue what to do.
 
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why WOULD it fall off at point B?

What's the shape of the path you WANT it to travel on?

Did you draw a Free-Body-Diagram of the coaster at B?
 
i posted a picture. Thats the link.
 
What I asked was, did YOU draw the Forces that act on the coaster,
and label them according to what caused them?
Why do we do that all the time?
 
YES. I DREW A FREE BODY DIAGRAM. It would fall off if the weight did not equal the centripetal force.
 
so set the weight equal to m v^2/r, and solve for v needed at top.

Now, how to get that speed there ...
have you done PE and KE , yet? that's the best approach here.
 
we just started pe, and ke
 
perfect.
The PE_gravitational at the start (height H) + Work done by friction (=0)
becomes PE_grav + KE at point B.

What's the height at B? What KE did you need there?
 
Last edited:

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