Momentum or Kinetic Energy to find Acceleration?

[God Plays Dice]

I also used the relativistic equations and they give the same non compliance

 

[nasu]

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.

 

[God Plays Dice]

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?

 

[God Plays Dice]

Can the craft pick up more KE than is supplied to the particles?

 

[gleem]

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.

 

[Let'sthink]

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!

 

[Kaushik Sinha]

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.