Roller Coaster Friction Problem

AI Thread Summary
The discussion revolves around a roller coaster's ability to complete a loop after descending from a 90m hill and encountering a 20m rough patch with a friction coefficient of 0.8. Key calculations involve determining the centripetal acceleration and the forces acting on the coaster, particularly how friction affects energy conservation. The potential energy at the hill's height suggests the coaster has enough energy to reach the loop, but friction must be factored into the energy calculations. Participants emphasize the importance of using work-energy principles and calculating the minimum speed required at the loop's top to ensure successful navigation. Understanding these concepts is crucial for solving the problem effectively.
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Homework Statement




A roller coaster begins with a 90m hill followed by a 40m diameter loop. Unfortunately, the coaster hits a 20m long rough patch between the bottom of the hill and the loop. If the friction on the rough patch is .8, then can a roller coaster make it through the loop?


Homework Equations





The Attempt at a Solution


I found that the centripetal acceleration is 9G's and that the weight a person would feel would be 10G's, but I don't know the equation I would use and how to factor in friction.
 
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The concept of the problem is about conservation of energy.
Taking ground as zero reference of PE.
PE at 90m surely can make a loop of height 90m.
You have to calculate if the extra energy going for 40m loop is exceeding the energy use by frictional force for the given distance.
 
Do you know the equation?
 
That's quite a coaster you got there with 10 g's at the bottom of the loop...without friction. Are you familiar with work-energy methods and minimum speed required at the top of the loop to make it through the loop?
 
Afraid not
 

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