Im doing a science project where need to know how fast a ship would go if we used a nanogram of positrons and a nanogram of electrons for propuslion (AMAT annihilation). Also, what would be the best mass for a space ship going at that speed?

Thanks for the help (im kinda a n00b at this stuff)

--emalius

Originally posted by emalius
Im doing a science project where need to know how fast a ship would go if we used a nanogram of positrons and a nanogram of electrons for propuslion (AMAT annihilation). Also, what would be the best mass for a space ship going at that speed?
Well, the energy liberated would be E = (m_e-m_e+)c² = (2 x 10^-12 kg)*(9 x 10¹⁶ m²/s²) = 180000 J.

If you had a perfect engine that could convert all of this energy into kinetic energy of the ship, and the ship started at rest, then the ship would have a velocity such that

KE = (<font face="symbol">g</font> - 1) m₀ c²

where KE is the same energy as liberated above, and m₀ is the rest mass of the ship, and <font face="symbol">g</font> is 1 / (1 - v²/c²).

If your ship is about the size of the space shuttle, with a mass of about 2 million kg, then it turns out that gamma is essentially 1; it's only different by 1 part in 10¹⁸. This means the ship won't be going fast enough to need to be treated relativistically, after all.

To simplify the numerics, we can ignore the gamma and fall back to the Newtonian kinetic energy

KE = (1/2) m₀ v², and solve for v to find that the ship is travelling at about 0.4 m/s.

We arrive at the conclusion that two nanograms of mass aren't equivalent to enough energy to accelerate a 2 million kg spacecraft by very much at all.

- Warren

thank you so much. this helps a lot. also, would there be any difference in speed if the ship was launched from the earth like a standard rocket and then used AMATA (AMAT annihilation) for boost?

Originally posted by emalius
thank you so much. this helps a lot. also, would there be any difference in speed if the ship was launched from the earth like a standard rocket and then used AMATA (AMAT annihilation) for boost?
You're capable of adding kinetic energies, aren't you?

- Warren

err actually, im in 8th grade, although im very interested in physics and would appreciate if some one could show me

awesome! this is a cool thread. i appreciate the interest shown by emailus and the intelligence shown by chroot.

Originally posted by emalius
err actually, im in 8th grade, although im very interested in physics and would appreciate if some one could show me
Okay, well... all you need to do is remember that velocity and kinetic energy are related. If you increase the kinetic energy, you increase the velocity.

So you take the kinetic energy of the craft after it's exhausted its rocket fuel, and add on the energy from the anti-matter propulsion system (assuming 100% efficiency). Once you have the total kinetic energy, you can use it to solve for the velocity, as I showed in my last post.

- Warren

errr still dont get it sry. its ok, u dont have to try to explain it to me

Originally posted by emalius
errr still dont get it sry. its ok, u dont have to try to explain it to me
It's okay, I'll help. I didn't realize you were in 8th grade, or I probably wouldn't have been so...... clinical in my solution above.

Give me some specifics on the problem, and I'll try to help you understand how to solve it.

If you're talking about launching your craft from a rocket like the space shuttle, you can assume some things. The space shuttle ends up going about 8000 m/s when it's in orbit.

If you only have two nanograms of antimatter though, you're only going to be able to accelerate your craft an additional 0.4 m/s... for a total speed of 8000.4 m/s.

- Warren