Energy conservation of a rod in free space

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Discussion Overview

The discussion revolves around the conservation of energy in the context of a rod with uniform density in free space when subjected to impulses applied at different points. Participants explore the implications of applying impulses at the center of mass versus off-center, particularly focusing on the resulting translational and rotational energies.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant, Volker, proposes that applying an impulse at the center of mass results in translational energy of E=1/2mv^2, while an off-center impulse results in both translational and rotational energy, leading to confusion regarding energy conservation.
  • Another participant clarifies that the same impulse implies a force applied over a given time, but the distance traveled by the point of application varies depending on where the force is applied, affecting the energy transferred to the rod.
  • A reference to a similar discussion on external forces acting on a rigid body is made, suggesting that this topic has been explored previously.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the implications of energy conservation in the scenarios described. There is acknowledgment of differing perspectives on how energy is transferred based on the point of application of the impulse.

Contextual Notes

There are unresolved assumptions regarding the definitions of impulse and energy transfer in the context of rigid body dynamics, as well as the implications of applying forces at different points on the rod.

Volkr16
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Hey everyone,

A meager pea brain (me) is in need of some help from you fine physics gentlemen.
This is a concept I've spend a lot of time pondering on (more than I would like to admit).

Imagine a rod of uniform density in free space. If you apply impulse onto the center of mass then it will gain an energy (transverse) of E=1/2mv^2. If you apply an impulse off the center of mass then it will gain an energy of E=1/2mv^2+1/2Iw^2 (transverse+rotational).

Here is what I think I know: Let's assume that this rod gets hit perpendicular to it's length. No matter where it gets hit, the center of mass will have equal transverse motion for equal impulse applied. In other words Ft=mv for center of mass

So let's assume two scenarios, one where the impulse is applied off the center of mass and one where it is on the center of mass. Make the impulse be so, that the velocity of the center of mass will be the same in both cases (From what i stated before i should be able to use the same impulse anywhere on the rod).

My problem lies in the conservation of energy: I know if the impulse is applied off center i will have rotational energy, but i also know that I will have the same translational energy no matter where the rod get hit (perpendicular on the length). Something isn't right here.

Surely my "what i think i know" must be wrong. Could someone please elaborate why?

Thanks in advance,

Volker
 
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The same impulse means applying a given force for a given time. Depending on where you apply the force, the distance that the point of application travels during that time will be different - and the energy transferred to the rod is equal to the force times the distance, not the force times the time.
 
Thanks guys, that cleared it up. I searched a lot before posting this, but didn't find that thread - sorry
 

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