How to Solve for an Object's KE and Heat in a Differential Equations Problem?

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Homework Help Overview

The discussion revolves around finding the kinetic energy (KE) and heat of an object in the context of a differential equations problem involving forces such as air drag and gravity. The problem is framed as an initial value problem, with specific parameters provided for the object's motion.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the formulation of a differential equation related to the forces acting on the object, questioning the appropriateness of the initial equation proposed. There is an exploration of how to relate kinetic energy to the motion of the object, with suggestions to focus on velocity rather than position.

Discussion Status

The discussion is ongoing, with participants raising questions about the correct initial value differential equation to use and how to derive it from Newton's laws. Some guidance has been offered regarding the use of Newton's second law, but there is no consensus on the approach yet.

Contextual Notes

Participants are grappling with the relationship between kinetic energy, forces, and the appropriate mathematical representation of the problem, indicating potential gaps in understanding the connections between these concepts.

steven452
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Homework Statement



We're supposed to find the object's KE and heat. Given:

Forces on Object: Air Drag + Gravity
Air Drag = .5(coefficient of drag)(1.2 kg/m3)v2A
A = cross sectional area
R = Radius of object
Object is X Km above the ground
Initial velocity = V

We are told it should be an initial value problem.

Homework Equations



Possibly y"+ (Force due to Drag)y' + (gravity)y = 0

The Attempt at a Solution



I tried plugging in the initial conditions to the equation above, but I'm stuck at that point.
 
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Possibly y"+ (Force due to Drag)y' + (gravity)y = 0
How did you get that equation?

Since kinetic energy has nothing to do (directly) with position, you shouldn't have to solve for y (which I'm assuming stands for the height of the object); instead, focus on v(t), and don't forget that a(t) = dv/dt
 
I just sort of assumed that's the equation we had to use, but I wasn't sure?

What initial value differential equation should I be using?
 
You should be able to derive an equation using Newton's second law and what you know about the forces acting on the object
 
I was originally going to do it entirely with Newton's laws, but I'm having a hard time seeing how Newton's equations can "convert" into DE?
 

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