Answer to Question #52488 in Mechanics | Relativity for Helen

Question

A spaceship of mass 2.40 x 10^6 kg is to be accelerated to a speed of 0.700c. (a) What minimum amount of energy does this acceleration require from the spaceship's fuel, assuming perfect efficiency? (b) How much fuel would it take to provide this much energy if all the rest energy of the fuel could be transformed to kinetic energy of the spaceship?

Answer 1

Solution:
Given:
m = 2.4 10^6 kg
v = 0.7c
(a) What minimum amount of energy does this acceleration require from the spaceship's fuel, assuming perfect efficiency?
Solution a.
E= mc^2/sqrt(1-(v/c)^2)
MATLAB CODE:
c = 2.998e8;
v = 0.7*c;
m = 2.4e6;
E = m*c^2/sqrt( 1 - (v/c)^2)
MATLAB OUTPUT:
E = 3.0206e+23 = 3.02*10^23 (J)
(b) How much fuel would it take to provide this much energy
if all the rest energy of the fuel could be transformed to kinetic energy of the spaceship?
Solution b.
Let's assume that Heat of Combustion for Space fuel delta H = 6100 000 J/kg
m = E/ delta H = 3.023 10^23/ 6.1 * 10^6 = 4.95 *10 ^16 kg