T-Mobile Wi-Fi 9:58 AM courses1.webwork.maa.org An ion thruster uses electric fi

Question

T-Mobile Wi-Fi 9:58 AM courses1.webwork.maa.org An ion thruster uses electric fields to accelerate positively charged xenon ions. These ions are the exhaust that provide thrust to a spacecraft. The xenon ions used for propellant have a mass of 2.190 x 1025 kg and a charge of 8.651 x 1018 C For all parts, assume the direction of motion of the accelerating particle is the +x direction. (A) What uniform electric field is needed to accelerate the xenon ions from rest to 4.64 × 106 m/s in a distance of 1 .21 mm? (B) How long does it take to accelerate the xenon ions from rest to 4.64 × 100 m/s in a distance of 1.21 mm? (C) A separate beam of electrons is used to inject electrons into the xenon exhaust to prevent the spacecraft from charging (i.e. to keep the spacecraft neutrally charged). What uniform electric field is needed to accelerate the electrons from rest to 464 × 106 m/s in 522 ps? Hint: 1 ps = 1 × 10-12 s

Explanation / Answer

A).

Using 3rd equation of motion

v^2= 2*a*d

a= (4.64*10^6)^2/(2*1.21*10^-3)

a= 8.897*10^15 m/s^2

Applying equilibrium of force

qE= ma

E= 2.19*10^-25* 8.897*10^15/(8.651*10^-18)

E= 2.25* 10^8 N/C

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t= v/a= 4.64*10^6/(8.897*10^15)

= 5.215*10^10 seconds.

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E= ma/q

= 9.1*10^-31* 8.897*10^15/(1.6*10^-19)

= 50601.69 N/C

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Comment in case any doubt..goodluck

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