Question

How much energy is required to accelerate a spaceship with a rest mass of 128 metric tons to a speed of 0.581 c? Hints: In the acceleration process the energy we have is converted to the kinetic energy of the spaceship. The classical kinetic energy of an object is half of the mass multiplied by the square of the velocity. What is the relativistic form of the kinetic energy? Incorrect. Tries 2/20 Previous Tries Every day our Earth receives 1.55×1022 J energy from the Sun. If we were able to use 0.75 percent of this energy to accelerate spaceships, then how many missions would be possible in one year?

Answer 1

given

m_o = rest mass of 128 metric tons

= 128 tons

= 116120 kg

v = speed of 0.581 c

E = 1.55 x 10²² J  

75 percent = 0.75

KE = [ m_o C² / ( 1 - v² / C² )^1/2 ] - m_o C²

= [ 116120 x C² / ( 1 - 0.581² C² / C² )^1/2 ] - 116120 x C²

= [ 116120 x C² / ( 1 - 0.581² )^1/2 ] - 116120 x C²

= [ 116120 x C² / 0.8139 ] - 116120 x C²

= 26528.974 x ( 3 x 10⁸ )²

KE = 2.387 x 10²¹ J

E = 1.55 x 10²² J per day

= 1.55 x 10²² x 365 x 0.75 /100

E = 4.2431 x 10²² J

n = E / KE

= 4.2431 x 10²² / 2.387 x 10²¹

n = 17.75 missions will be possible in one year