Conservation of energy / work problem

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Homework Help Overview

The discussion revolves around a conservation of energy problem related to a height difference in a hill scenario. Participants are examining algebraic manipulations and the interpretation of initial and final positions in the context of energy conservation.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are questioning the algebraic steps taken to simplify the expressions related to initial and final heights. There is also a focus on identifying the correct values for initial and final positions in the context of the problem.

Discussion Status

The discussion is active, with participants seeking clarification on the problem statement and algebraic processes. Some guidance has been offered regarding the identification of variables, but there is no explicit consensus on the correct approach yet.

Contextual Notes

There is a mention of a height difference of 30m, which is central to the problem, but the exact formulation of the problem statement remains unclear. Participants are also reflecting on their algebraic workings and potential errors.

adams_695
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Homework Statement
Call the system the bicycle and the rider. Use the work-energy equation and W = Fd. Assume the cyclist and air do not heat up. The work-energy equation is Kf + Ugf = Ki + Ugi + W.
Relevant Equations
Kinetic energy & gravitational energy
Answer- Physics .jpg
Attempt 1- Physics.jpg
Attempt 2- Physics.jpg

If someone could advise what I've done wrong it would be much appreciated. How have they eliminated the initial and final for y, and simplify only to y? Also, how did they simplify to a positive 2? What algebraic steps have I missed? Thanks for your help.
 
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I would not call that a problem statement. What is the actual question?
 
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haruspex said:
I would not call that a problem statement. What is the actual question?
695672E7-6A77-4F8D-8425-24ED89C62321.png


Sorry here it is. Question 9. Thanks!
 
You are told the top of the hill is 30m higher than the bottom of the hill. So what is yi-yf?
 
haruspex said:
You are told the top of the hill is 30m higher than the bottom of the hill. So what is yi-yf?

30m-0m.

Is this how I went wrong when solving algebraically in the image of my working?
 
There was nothing wrong in what you worked out. As haruspex pointed out, identify yi and yf in your own algebra and you are done.
 
adams_695 said:
30m-0m.

Is this how I went wrong when solving algebraically in the image of my working?
The last line of your working has the terms -2gyf+2gyi. Factorise.
 

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