Momentum or Kinetic Energy to find Acceleration?

[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.