Is Velocity Equal to Work Divided by Impulse in Physics?

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Discussion Overview

The discussion revolves around the relationship between velocity, work, and impulse in physics. Participants explore whether velocity can be derived from the division of work by impulse, examining the implications of this relationship within the context of classical mechanics and touching upon concepts from relativity.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that dividing work by impulse leads to the conclusion that velocity equals delta d divided by delta t, questioning the validity of this reasoning based on cancellations.
  • Another participant clarifies the definitions of work and impulse, relating them to energy and momentum, and introduces the relationship E = pc for photons, indicating that dividing energy by momentum yields velocity.
  • A participant connects the equation E = pc to the famous equation E = mc², expressing confusion about relativity but finding the explanation helpful.
  • One participant reiterates the initial claim about dividing work by impulse, presenting additional equations related to kinetic energy and momentum, and suggests that velocity does not equal work divided by impulse.
  • Another participant challenges the equivalence of momentum and mass in the context of energy and momentum relationships, emphasizing the distinction between them.
  • Some participants express surprise at the discussion veering into relativity, given the original focus on classical mechanics.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether velocity can be equated to work divided by impulse. There are competing views regarding the validity of the initial claim and the implications of introducing relativistic concepts.

Contextual Notes

The discussion includes assumptions about the definitions of work, impulse, energy, and momentum, which may not be universally agreed upon. The transition to relativistic concepts introduces additional complexity that remains unresolved.

lonelypancreas
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Since Work = F*delta(d) and Impulse = F*delta(t) then dividing work over impulse, through simple cancellation of F we can say that it is now equal to delta d / delta t which is equal to velocity right? My question is, does this make sense "physics-wise" since I onlu arrived at my answer through cancellations?
 
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Hi lonely:

Your equations should be:
delta(Work) = F*delta(d)
delta(Impulse) = F*delta(t)​

delta(Work) is an infinitesimal of Work = an infinitesimal of energy = ΔE
delta(Impulse) is an infinitesimal of Impulse = an infinitesimal of momentum = Δp​

From
In empty space, the photon moves at c (the speed of light) and its energy and momentum are related by E = pc, where p is the https://www.physicsforums.com/javascript:void(0) of the momentum vector p.

Consider a photon which has momentum p and energy pc.
The result of dividing the photon's energy by its momentum gives its velocity c.

Hope this helps.

Regards,
Buzz
 
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E = pc is the same as E = (mc)c --> E = mc^2 right? I still haven't encountered relativity so I'm not quite familiar with that famous equation but I think through your answer, it made sense. Thanks.
 
lonelypancreas said:
Since Work = F*delta(d) and Impulse = F*delta(t) then dividing work over impulse, through simple cancellation of F we can say that it is now equal to delta d / delta t which is equal to velocity right? My question is, does this make sense "physics-wise" since I onlu arrived at my answer through cancellations?

If you have ##KE = \frac{1}{2}mv^2## and ##p = mv##, then

##\frac{KE}{p} = \frac{1}{2}v##

And:

##KE = \frac{p^2}{2m}##

You might like to think about why

##v \ne Work/Impulse##
 
lonelypancreas said:
E = pc is the same as E = (mc)c --> E = mc^2 right?

No, because p ≠ mc.

The general relativistic relationship between energy, momentum and (rest) mass is E2 = (pc)2 + (mc2)2. Set m = 0 and you get E = pc.
 
Given this was a post on classical mechanics in the Classical Physics section, I'm not sure how we ended up talking about relativity!
 
PeroK said:
Given this was a post on classical mechanics in the Classical Physics section, I'm not sure how we ended up talking about relativity!

Because this is PF. You can't write down an inclined plane problem without someone chiming in about GR.
 
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