Ball rolling down a segment then up a parabolic segment

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Homework Help Overview

The problem involves a 181 g ball released from a height of 5.19 m, rolling down a 21° incline and then up a parabolic segment defined by the equation y=x²/4. The objective is to determine how high the ball will ascend on the parabolic segment before reversing direction.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of energy conservation principles, questioning the initial and final states of kinetic and potential energy. Some express uncertainty about their calculations and the implications of the parabolic shape on the ball's motion.

Discussion Status

There is an ongoing exploration of the problem, with participants reflecting on their approaches and the potential misinterpretation of the parabolic segment's impact on energy conservation. Some guidance has been offered regarding the understanding of energy conservation in this context.

Contextual Notes

Participants note confusion stemming from the problem's setup and the additional information provided, which may have led to overthinking the solution. There is an acknowledgment of the challenge posed by the parabolic segment in relation to energy conservation.

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Homework Statement


A 181 g ball is released from rest H=5.19 m above the bottom of the track shown in Figure. It rolls down a straight 21° segment, then back up a parabolic segment whose shape is given by y=x2/4, where x and y are in m. How high will the ball go on the right before reversing direction and rolling back down?
C10P81.jpg


Homework Equations


Ki+Ui=Kf+Uf
K=mv^2/2


The Attempt at a Solution


I am not sure how to start this because everytime i go to one direction i hit a dead end.
At the beginning it has both Ki=0 and Ui=0 correct?
Then at the final it has Kf and Uf right?
 
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Here is my work but I don't even think I am on the right track...

This is for rolling down incline
Physics7.jpg



This is for rolling up the parabola
Physics8.jpg

EDIT: I put the wrong dominator in for the very last part when calculating Y it should be 4, but that anwser did not work either
 
WOOOOOOW I am so sorry for wasting everyones times the parabola made me over think this equation since Ki+Ui=Kf+Kf...energy would force the ball up the same height as it began.
 
The question gave you additional information to deceive you. Realizing this in the end only makes you understand energy conservation better. It's hardly wasting anyone's time.
 
Yeah, I see what you mean but I didn't need to make a thread after.
 

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