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In: Physics

A spaceship initially at rest is propelled to a Lorentz factor ? = 8 (speed of...

A spaceship initially at rest is propelled to a Lorentz factor ? = 8 (speed of 0.9922c). The mass of the spaceship is 20,000 kg; neglect the mass of the fuel.

a. How much energy (in J) would be required to do this? [Hint: Use equation (9-5). Your answer will be in joules (J) if you use c =3.0 ?108 m/s, since 1 J = 1 kg m2/s2.] [2 points]

b. How much mass in fuel would be needed to create this much energy at the highest possible efficiency, 100% conversion of rest-mass into energy? [Hint: Use the equation E = mc2 and solve for m.] [1 point]

c. Was our neglect of the mass of the fuel correct in this case, or is much more mass needed in fuel than in the structure of the spaceship? That is, can space travel near the speed of light be fuel-efficient? [1 point]

Solutions

Expert Solution

A) The kinetic energy of the rocket =

, this is the amount of energy required to put the rocket in this state.

B) if the mass of fuel is mf then,

this is the amount of the fuel.

C) The mass of the fuel is definitly much more than the mass of the spaceship itself. So our initial assumption was not correct. i.e. Space travel near the speed of light is not fuel efficient.

genius_generous answered 2 years ago
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