Momentum or Kinetic Energy to find Acceleration?

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Discussion Overview

The discussion revolves around the calculation of acceleration for charged particles (protons) accelerated by an electric field, specifically comparing the use of momentum and kinetic energy in these calculations. Participants explore the implications of using each method and the discrepancies that arise between the two approaches.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants propose using the change in momentum per second to find acceleration as dp/dt / M = a.
  • Others suggest calculating acceleration from kinetic energy using Sqrt(KE/t / 0.5*M) = a, but this is challenged as incorrect.
  • A participant questions the validity of the kinetic energy approach, noting that it yields values significantly larger than those from momentum calculations.
  • Concerns are raised about the high power requirement and the resulting acceleration, with some participants noting discrepancies in the values derived from kinetic energy and momentum.
  • There is discussion about the implications of relativistic effects on the calculations, with some participants asserting that relativistic equations lead to different results for momentum and kinetic energy.
  • One participant mentions that the kinetic energy derived values are consistently higher than those from momentum, even for slow-moving protons.
  • There are multiple inquiries about how thrust is calculated and whether conservation of momentum applies in this context.
  • Some participants express confusion over the relationship between momentum and kinetic energy, questioning how they can yield different acceleration values.
  • One participant emphasizes that not all energy goes into the motion of the objects, referencing inelastic collisions as an example where momentum is conserved but kinetic energy is not.
  • A later reply introduces a more complex equation involving relativistic mass, suggesting a more nuanced approach to the problem.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether kinetic energy or momentum is the appropriate method for calculating acceleration, with multiple competing views and unresolved discrepancies remaining throughout the discussion.

Contextual Notes

Participants note that the calculations depend on assumptions about the system, including whether relativistic effects are considered and the nature of the forces involved. There are unresolved mathematical steps and dependencies on definitions that contribute to the differing results.

  • #31
I also used the relativistic equations and they give the same non compliance
 
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  • #32
God Plays Dice said:
Yes. I take the sum of all the particles in terms of momentum, ie their mass X vel and then divide thru by mass of the craft. I'm sure this is correct. Then I take the sum of all the particles 0.5 mass X vel^2. And rearrange this equation to find vel of the craft plugging in mass of craft. When the vel of the particles is very high then the KE vel is much higher than the momentum vel. When the vel of the particles is quite slow I get a KE vel slower than momentum vel. Do the excel sheet yourself it takes only a couple of minutes just plug any mass values in and do a range of particle velocities youl get non compliant KE vel with p vel.
There si no point to repeat. The second method is not valid.
There is no momentum velocity and KE velocity.
 
  • #33
But how can something have a velocity that's described by its momentum, and at the same time not have the required KE for the job?
 
  • #34
Can the craft pick up more KE than is supplied to the particles?
 
  • #35
God Plays Dice said:
But how can something have a velocity that's described by its momentum, and at the same time not have the required KE for the job?

Not all Energy goes into the motion of the objects. Consider an inelastic collision. Momentum is conserved but KE is not.
 
  • #36
In the nonrelativistic limit
KE =E say = (p^2)/(2m) We have
dE/dt = [{2p(dp/dt)}/2m
So Force = [(dp/dt)/m] = (1/p)*(dE/dt)
So no square roots please!
 
  • #37
God Plays Dice said:
Hi all,

I have charged particles (protons) accelerated by an electric field. If I add up all the momentum and find the change in momentum per sec I can find the acceleration of my craft by
dp/dt /M = a

If I add up all the kinetic energy of the particles and find the KE per sec, I can find the acceleration by
Sqrt (KE/t /0.5*M) = a

They are both similar calcs but give wildly different values. KE calc is 10^9 bigger.

So which is it? KE or p to find acceleration?
at that magnitude dp/dt =mdv/dt + vdm/dt i.e ma + vdm/dt.
here m = Mo/sqrt(1-v^2/c^2),
Mo is rest mass of the particle.
Please try this.
 

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