Kinetic and poetenial energy of a roller coaster loop

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Homework Help Overview

The discussion revolves around a physics problem involving the kinetic and potential energy of a roller coaster as it travels down an incline and through a loop. The original poster describes the scenario of an object of mass m moving down an incline and entering a loop, with a focus on calculating the normal force as a function of the angle ө, given specific parameters such as mass, gravitational acceleration, height, and radius.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand how to formulate the problem into equations, expressing uncertainty about whether to use multiple equations or a single equation to represent the different angles. Some participants question the behavior of the equation at specific angles and whether the relationship resembles a sine function. Another participant raises inquiries about the forces acting on the body at the apex of the loop and their directions as the body moves along the loop.

Discussion Status

The discussion is ongoing, with participants exploring different aspects of the problem. There is an acknowledgment of the complexity involved in formulating the equations, and some guidance is being sought regarding the forces at play during the motion through the loop. Multiple interpretations of the problem are being considered, particularly regarding the relationship between energy and angle.

Contextual Notes

Participants are working within the constraints of the problem as posed, including the requirement to check the behavior of the equation at specific angles (0, 90, and 180 degrees) and the assumption that the height is a critical factor in the calculations. There is an indication that a visual aid may be beneficial for understanding the problem setup.

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Homework Statement


O.k, i'll do my best to explain the problem as I but a picture would probabley be helpful. Basically there's an object of mass m travlleing down an incline. Near the end of the incline it does a loop. The question asks to calculate the normal force(Fn) as a function of ө for 0 ≤ ө ≤ 180 (assume cart is from height h) hint: your answer will depend on m, g, h, r and ө. Check that equation has proper behavior ө= 0 degrees, 90 degrees and 180 degrees.


Homework Equations




U= mgh

k=1/2mv^2


The Attempt at a Solution



i understand what's going on it's just putting it into an equation that I find difficult. I am assuming that ө equals zero at the appex before the ascent into the loop. Also, kinetic energy increase as ө increase i think. I'm just no sure if I should do three separate equations or one if just one then how can it represent all three angles? Any help will be greatly appreciated!
 
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After looking at this problem some more I see that the equation kind of looks like the sine function am I on to something?
 
Please could someone help me?
 
When the body reaches the appex of the loop ita velocity will be v = sqrt(2gh). What are the forces acting on the body at this point and what are there direction? As the body moves along the loop, what are the directions of these forces?
 

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