# Momentum or Kinetic Energy to find Acceleration?

1. Dec 23, 2015

### God Plays Dice

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?

2. Dec 23, 2015

### gleem

This is not correct

3. Dec 23, 2015

### God Plays Dice

4. Dec 23, 2015

### God Plays Dice

Is it more like
Sqrt(KE/0.5*M) / t = a

5. Dec 23, 2015

### gleem

Power = dK.E./dt = Fv= mav

a = (dK.E./dt)/p

6. Dec 23, 2015

### God Plays Dice

cheers, its in the right ballpark now

7. Dec 23, 2015

### God Plays Dice

The only problem now is that I have a system with a ridiculously large power requirement, 5E+14W, with not a very large final acceleration of 23m/s^2 of a 100 ton craft. Something is still wrong

8. Dec 23, 2015

### God Plays Dice

No wait, problem still exists, I didnt put brackets in

9. Dec 23, 2015

### God Plays Dice

The KE accln is actually 10^4 over the momentum accln

10. Dec 23, 2015

### gleem

So you are producing a force of 2.3E6Nt assuming the mass is 100 metric tons ie. 105Kgs and needing 5E+14 watts you get a velocity greater than that of light!!!!???? did you consider that the protons might be relativistic? What is the accelerators potential difference?

11. Dec 23, 2015

### God Plays Dice

I have used relativistic equations. I have accelerated protons to 0.99c. Do the mathematics, find momentum and KE (relativistic) of these then you will see that when you try to get acceleration or velocity even from these two they differ greatly.

12. Dec 23, 2015

### God Plays Dice

The momentum values seem more real, I dont know where that huge KE comes from, gamma is only around 7.

13. Dec 23, 2015

### God Plays Dice

In fact the discrepancy is there even with slow moving protons, the KE derived values are far greater than those taken from p.

14. Dec 23, 2015

### gleem

So how did you calculate the thrust?

15. Dec 23, 2015

### God Plays Dice

I havent calcd thrust. Just taken the momentum or KE of the particles and assumed that is the same on the craft

16. Dec 23, 2015

### God Plays Dice

Surely that must be right for momentum at least, straight conservation of momentum

17. Dec 23, 2015

### God Plays Dice

I suppose I did calc thrust, when I found momentum delivered to particles per sec

18. Dec 23, 2015

### gleem

But the momentum is constantly changing. So you need to consider the rate of change of momentum and not just the momentum.

the proper way to solve the rocket problem is to say that the force ie thrust is the rate of change of momentum which in this case is the rate at which the mass of protons is being expelled times their velocity. and this is equal to the rate of change of the momentum of the rocket.

vprotonsdmprotons/dt = Mrocketa

19. Dec 23, 2015

### God Plays Dice

I got that. Conservation of momentum. However I also found the KE of the particles, which seems very very high, and found the acceleration from that Power and it turns out a totally different value to the one from momentum. Its way higher. So I have two questions, or really just one. Why are they different and why is the KE so high, its 10^14W! This serves a momentum that can only move 100 ton at 22m/s^2.

The saturn 5 rocket was 10^11W and was 3000 ton.

20. Dec 23, 2015

### gleem

KE is measure in joules and power is measured in Joules/sec. You need a time (of burn) to convert one to the other

21. Dec 23, 2015

### God Plays Dice

Well i brought the proton speed down from 0.99c to around 3000m/s, seems to have done the trick I not stuck with an impossible power requirement now

22. Dec 23, 2015

### gleem

That should not have been a problem for now you are non relativistic. So maybe your relativistic approach was the problem.

23. Dec 24, 2015

### God Plays Dice

I did the calc in Newtonian. Still same result KE differs from momentum

24. Dec 24, 2015

### gleem

I don't understand this statement?

25. Dec 24, 2015

### gleem

Are you assuming that the acceleration is constant because the power is constant? It is not. As the vehicle speeds up the acceleration decreases.