Question

miro photons Problem #2 Photon propulsion. Star Trek Enterprise impulse propulsion is powered by nuclear fusion. As we have seen, only about 1% of the fusion fuel mass is converted into energy. A more efficient engine for sub-luminal travel is under development, which uses matter-antimatter annihilation with 100% mass-to-energy conversion. The diagram below illustrates the principle of the new photon propulsion engine. Assume that the mirror system is perfect and sends all photons in one direction. annihilation a) What is the combined energy of all the photons created by burning one tonne (1000 kg) of fuel (i.e. 500 kg of matter 500 kg of antimatter)? How much momentum do these photons carry? b) Fully-loaded with its matter-antimatter fuel, Enterprise weighs 100,000 tonnes. In the beginning, the Enterprise is at rest with respect to Earth. Then, in one quick burst, it burns 10,000 tonnes of its fuel. Sketch the energy-momentum vectors of the Enterprise before the burst, the Enterprise after the burst, and the collection of photons created by the burst. Label the axes, show units. Feel free to use c 1 in this case. Use the energy momentum conservation law! d) Explain how a rocket ship (not necessarily the Enterprise with the photon propulsion, but a starship with some sort of propulsion) can accelerate uniformly forever without ever exceeding the speed of light

Answer 1

a) As it is a 100% mass to energy conservation ,the conservation of energy principle shows that the energy carried away by the photons equal to the rest mass of the fuel which implies it is= 1000*(c)^2.. Now when we see the process ,there are 2 photons resulting from the annihilation of a particle and an antiparticle.Each such processes obeys conservation of momentum and relativistic dispersion relation.As mass of photon is zero:

E²=(cP)²

=>E=cP

=>P=E/c

So then magnitude of momentum get added up in this fashion and we get

total momentum=(total energy)/c

(b) have taken c into account ri tal envigy mementuum ve dr the frame which u wrt the earth guen by 74 adt ret CEOO0) R=10 whare 2. After the bust oul wit as the photon come mo mantum 10 S C thiu case igna the etket we granty Due to conuewation The momendtum Small momentun priniple the enterpise 10 c S C The diuecton beng oppait to the dirtchon ejecked photon) We can cenvidar the rocket bena prepelled rectns tve directum. the K-fdira The K-Puecm affer buut a Tiikal Anal Same Epmais remainingu 9 9x 10 00 10-G

d)The reason why the rocket can accelerate uniformly with out reaching the speed of light is because when we consider moving object we consider its relativistic mass . In classical scenario this addition factor multiplied to the rest mass is nearly equal to one but when greater and greater speeds are reached the value of this relativistic mass increases exponentially,hence more force is required to bring the same change in speed for a body moving with a greater velocity .