Protons to accelerate a space probe

[josephcollins]

Okay ppl, I have a question, I'd just like you to check that my working here is correct.

Q: A space probe of mass m=490kg is driven by an ion propulsion motor that involves the use of positive ions, each of mass m=2.18*10^-25 kg and having a charge of magnitude e=1.6*10^-19 C. These ions, having a negligible initial velocity, are accelerated by a potential difference of magnitude 1.2*10^3 V that exists between two electrodes which are a distance of 5cm apart. The ejection of these accelerated ions from the space probe generates a forward thrust that drives the probe.


I got the velocity with which the ions leave the probe, using the argument that kinetic energy and velocity are equal. So mv^2=QV and v turns out to be 419169.8 m/s

Then I had to calculate the Force exerted on the ions when the number of ions between the electrodes is 2*10^13. This I did by saying that F=EQ, and since E=V/separation, F=VQ/separation. I got an answer of 0.0768N.

Lastly I had to calculate the time taken to accelerate the probe from 0 to 100km/h. I did this by first getting the acceleration of the probe. It is equal to F/m where F=0.0768N and m=490kg. so a=1.567*10^-4 m/s^2. Then I used (v-u)/a gives the time and set v= 100000/3600 and used the accn just calculated to get a time of 49.23 hrs. Could someone just verify that I did this correctly in terms of the logic involved?

Thanks, Joe

 

[Soveraign]

I get the same final answers you do, 49.23 hours to get to 100km/h but $\frac 1 2 m v^2 = QV$ gives 4.197 x 10^4 m/s.


$$v = \sqrt{\frac{(1.6 \star 10^{-19})(1.2 \star 10^3)}{(.5)(2.18 \star 10^{-25})}}$$

 

[wais]

Your working seems to be correct. You have correctly calculated the velocity of the ions leaving the probe and the force exerted on them. Your calculation for the acceleration of the probe and the time taken to reach a speed of 100km/h also seems to be correct. Overall, your reasoning and calculations appear to be accurate and logical. Great job!