Calculus 1 Help: Solving Weight Formula for Distance

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Homework Help Overview

The discussion revolves around a calculus problem involving the weight of an object as it relates to its distance from the center of the Earth. The original poster is attempting to derive a formula based on the given information about weight and distance.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to establish a formula for weight in terms of distance but expresses uncertainty about the correct formulation. Participants question the use of the Earth's diameter in the context of the problem and seek clarification on the relationship between the diameter and the distance from the center of the Earth.

Discussion Status

The discussion is active, with participants exploring the implications of the given values and questioning the assumptions made by the original poster. There is no explicit consensus on the correct approach, but guidance is being offered regarding the interpretation of the problem.

Contextual Notes

Participants are discussing the relevance of the Earth's diameter in the context of the weight formula and the implications of using it as a reference point for distance.

sharingan80
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Okay I had a calculus test and we got it back and I got this question wrong. I tried it again but I can't figure it out.

The weight, w, in kg of an object is inversely proportional to the square of the distance, r, in km, from the center of the earth. Assume a stone of the ground has weight 100 kg and that the diameter of the Earth is approximately 12,756 km. What is the formula of w in terms of r?

I said w=k/r^2 but the question was multiple choice and I wasn't entirely sure so i chose the answer:
w=(100*12756^2)/r^2
but the right answer was
w= (25*12756^2)/r^2
 
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Why did you use the diameter for r? Where is the center of the Earth in relation to its diameter?
 
That's what I'm confused about. I don't know what 12,756 stands for in the equation.
 
You don't think it's coincidental that 12756 is also the value given for the diameter of the Earth in kilometers?

Ask yourself, if the diameter of the Earth is 12756 km, how far is the surface of the Earth from the center of the earth?
 

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