Need, quick answer, please Energy integral/derivative

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Homework Help Overview

The discussion revolves around deriving a relationship between time and position using the energy equation E=(1/2)mvr^2+U(r). Participants are tasked with solving for dt and setting up an integral, particularly in the case where E=0.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are questioning how to derive dt from the given energy equation and whether derivatives are necessary. There is also a mention of the relationship v = dr/dt as a potential starting point for the derivation.

Discussion Status

Some participants are exploring the derivation process and discussing the implications of the energy equation. There is a focus on understanding the role of velocity in relation to time and position, but no consensus has been reached on the method to proceed.

Contextual Notes

There is an assumption that energy remains constant, and participants are considering the implications of this assumption in their derivations. The specific context of E=0 is highlighted as a special case for exploration.

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Homework Statement



Start from this equation: E=(1/2)mvr^2+U(r)

and solve for dt. Set up the integral to find the relation between r and t, then carry out the integral in the special case that E=0.


Homework Equations





The Attempt at a Solution


HOW DO I GET DT? DO I HAVE TO TAKE THE DERIVATIVE OF THIS? IF SO, WITH RESPECT TO WHAT?

THANKS!
 
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briteliner said:

Homework Statement



Start from this equation: E=(1/2)mvr^2+U(r)

and solve for dt. Set up the integral to find the relation between r and t, then carry out the integral in the special case that E=0.


Homework Equations





The Attempt at a Solution


HOW DO I GET DT? DO I HAVE TO TAKE THE DERIVATIVE OF THIS? IF SO, WITH RESPECT TO WHAT?

THANKS!

t is time, and I assume you are trying to prove that energy remains constant using vector calculus. v = dr/dt.
 
i understand that dt is time, but now how to get dt.
 
I told you v = dr/dt.

I never went through all of this derivation, but I think that's the only dt there.
 

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