t poirt An lon thruster uses electric fields to elds to accelerate positively ch

Question

t poirt An lon thruster uses electric fields to elds to accelerate positively charged xenon ions. These ions are the exhaust that provide thrust to a spacecraft. The xenon positi ons usecd for propallant have a mas of 2.190 x10-25 kg and a charge of 8.651 x 10-18 C For all parts, assume the direction of motion of the accelerating particle is the +x direction A) What unitorm electric fiold is needed to accelerate the xenon lons from rest to 5.25 x 10 mls in a distance of 1.18 mm (8)How long does it take to accelerate the xenon ions from rest to 5.25 ×10° m/sinadistance of 1.18mm ? (G A segarate beam of lectrons a ued to nject electrons into thexenon exthaust to prevent he spacecrat from charging e.to kep the spacecrati neutrally charged). What uniform oloctric field is needed to accelerate the electrons from rest to 5.25 X 10 m/s in 450 ps? Hint lps = 1×10-12 s. Note: You can earn partial crodit on this problem

Explanation / Answer

a] By third equation of motion,

a = v^2/2s

= 5.25e6^2/[2*1.18e-3] = 1.168e16 m/s^2

E = F/q = ma/q = 2.19e-25*1.168e16/8.651e-18

= 2.96*10^8 N/C x^

b] using second equation of motion,

t = sqrt(2s/a) = sqrt(2*1.18e-3/1.168e16) = 4.495*10^-10 s

c] using first equation of motion,

a = v/t = 5.25e6/450e-12 = 1.167 *10^16 m/s^2

E = F/q = ma/q = 9.1e-31*1.167 *10^16/-1.6e-19

= - 66373 N/C x^

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