Calculus (infinite series) - Gravitational Potential Energy Problem

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Homework Help Overview

The discussion revolves around a problem related to gravitational potential energy, specifically involving infinite series in the context of calculus. The original poster expresses confusion regarding the physics concepts and the mathematical approach required to tackle the problem.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster seeks guidance on how to begin the problem, indicating a lack of familiarity with both physics and the necessary calculus concepts. Some participants suggest expressing the potential energy as a function of the ratio h/R and developing a power series expansion from there. Others inquire about the steps needed to manipulate the equations involved.

Discussion Status

Participants are actively engaging with the problem, offering hints and suggestions for approaching the series expansion. There is a focus on breaking down the problem into manageable parts, with some guidance provided on how to manipulate the equations. However, no consensus has been reached on a single method or solution approach.

Contextual Notes

The original poster mentions a lack of prior physics knowledge and limited experience with calculus, which may affect their ability to engage with the problem fully. There is also an emphasis on the need to understand the relationship between the variables involved in the gravitational potential energy equation.

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Homework Statement



[PLAIN]http://img818.imageshack.us/img818/817/potentialenergy.jpg


Homework Equations



Given above.

The Attempt at a Solution



I've never had physics in my life and am completely baffled by this problem. I'm only in calculus 3 and am just learning infinite series so I am supposed to be able to understand this on some level but I can't even figure out how to start. I'm not asking anybody to just give me the answer but if anyone can help me get started in the right direction I'd greatly appreciate it. I want to be able to comprehend this stuff but I don't feel like my calculus skills are there yet after only a few weeks. Thanks to anyone gracious enough to help!
 
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You don't need to know any physics to do this problem, just follow the hint. Figure out a way to express U as a function of h/R (and a bunch of constants), and then write out the power series expansion. This infinite power series is supposed to approximately equal -mgR + mgh.
 
So are you saying to solve U for both h and R, divide the two, then solve for U?
 
Try multiplying both the top and bottom of the equation by R so that you can factor another R out of the bottom, leaving you with a (-GmMR)/[R^2(1+h/R)]. Then use your GM/R^2 = 9.8 to end up with (-9.8mR)/(1-(-h/R)). From here, it's a simple power series of type a/(1-r).
 

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