Electrical potential involving a spacecraft

Homework Statement

Been stuck on this problem. Any help will be greatly appreciated

1. The (actual) spacecraft Deep Space 1 tested an ion drive engine in which Xenon atoms
were accelerated (maximum voltage of 1,300 volts), neutralized and used to provide
thrust. The probe carried 74 kg of Xenon and fired it engines for 678 days. The electrical
power was supplied by solar panels which were capable of delivering 2,100 watts to the
engines. The initial mass of the probe was 486 kg and the ion engine was started while
the probe was in orbit around the sun. From this data estimate;

a. Calculate or look up the mass of a single Xenon atom in kg.
.1313 kg

b. Assuming the Xenon atom is initially at rest what its velocity is after being accelerated through 1,300 volts.
i was thinking here to do conservation of energy involving electrical potential but it doesn't make sense

c. Using the data above, calculate the number of Xenon atoms that exited Deep Space 1 each second the drive was operating.

d. The Thrust of the engine (in Newton’s second) is the Newton’s 3rd law reaction to the change in momentum due to the exiting Xenon atoms. Calculate this trust by multiplying the total mass of the Xenon atoms that leave the spacecraft in one second (see a and c) times the exiting velocity (in m/2, see b).

e. Given that the initial mass of Deep Space 1, what was its initial acceleration.

f. Given the final mass of Deep Space 1 (when all of its fuel was spent) what was
the final acceleration before the engine shut down

The Attempt at a Solution

I have attempted at using conservation of energy in charge reactions but it doesnt seem to work. i need an equation involving velocity and voltage

berkeman
Mentor

Homework Statement

Been stuck on this problem. Any help will be greatly appreciated

1. The (actual) spacecraft Deep Space 1 tested an ion drive engine in which Xenon atoms
were accelerated (maximum voltage of 1,300 volts), neutralized and used to provide
thrust. The probe carried 74 kg of Xenon and fired it engines for 678 days. The electrical
power was supplied by solar panels which were capable of delivering 2,100 watts to the
engines. The initial mass of the probe was 486 kg and the ion engine was started while
the probe was in orbit around the sun. From this data estimate;

a. Calculate or look up the mass of a single Xenon atom in kg.
.1313 kg

b. Assuming the Xenon atom is initially at rest what its velocity is after being accelerated through 1,300 volts.
i was thinking here to do conservation of energy involving electrical potential but it doesn't make sense

c. Using the data above, calculate the number of Xenon atoms that exited Deep Space 1 each second the drive was operating.

d. The Thrust of the engine (in Newton’s second) is the Newton’s 3rd law reaction to the change in momentum due to the exiting Xenon atoms. Calculate this trust by multiplying the total mass of the Xenon atoms that leave the spacecraft in one second (see a and c) times the exiting velocity (in m/2, see b).

e. Given that the initial mass of Deep Space 1, what was its initial acceleration.

f. Given the final mass of Deep Space 1 (when all of its fuel was spent) what was
the final acceleration before the engine shut down

The Attempt at a Solution

I have attempted at using conservation of energy in charge reactions but it doesnt seem to work. i need an equation involving velocity and voltage

Welcome to the PF.

Your number in (a) is not right. Please re-check it. They are asking for the mass of a single atom.

Do you know if these atoms are singly-ionized? There is an equation to convert from keV to velocity (kinetic energy)...

Well the atomic mass of Xenon is 131.293 g/mol, so in kg it would be .1313kg/mol would it not?

Also for part b i have been trying to use the Kf + qVf = Ki + qVi (conservation of energy) but I do not know the value of the charge. So I'm thinking there might be an equation I am missing or something

A possible equation could be Voltage = E / q but once again i have no value for the charge

nasu
Gold Member
For (a) you have to calculate the mass of a single atom and not the molar mass. You'll need this to calculate the speed in (b).
When the meaning of the given voltage is that the ions are passed through a potential difference of such value. What is the work done by the electric field when an charge goes through a potential difference ΔV?

For (a) would it be .1313 divided by Avogadros number?

what about for part (b) i use the law of conservation which is Kf + qVf = Ki + qVi or Kf = Ki - qΔV and it starts from rest so Ki is 0,
essentially 1/2mv^2 = -qΔV
solve for v to find final speed

the problem is i don't know what the charge would be? Does neutralized mean it has no charge in the equation?

nasu
Gold Member
Yes, you will have to assume some charge for the ions.
And yes, neutralized means that they have no charge. But this happens after they are accelerated. So it has nothing to do with finding the speed.