How Do You Calculate Initial Acceleration in a Solar Propulsion Engine?

[koujidaisuki76]

A solar propulsion engine uses solar power to ionize atoms of xenon and to accelerate them. As a result of the accelerationprocess, the ions are ejected from the spaceship with a speed of 3.0E4m/s

Mass of spaceship is 5.4E2






Engine ejects 7.7E18 ions every second and the fuel mass is 81 kg. Lasts for 4.8E7 secs.


My question is how do you find th initial acceleration? The IB book says that its 8.2E-5 but I've been getting 9.3E-5

please help me! My IB test is tommrowo!

thank you!
:(

 

[Mindscrape]

You should show some work.

What do you know about how force relates to momentum, or what about momentum in general?

 

[koujidaisuki76]

momentum before and after collision is the same. the only that changes is velocity and the mass in certain cases (as this one) .

momentum is p=mv

conservation equation

mv+mv=mv+mv

okay:

so for the inital momentum of the feula nd rocket i said 0:

0: mv+mv
(81)(3.0E4) + (5.4E2)(v)<-- final velocity of spaceship

which is 4500

t is 48000000 so Acceleration:

4500/48000000 = which is 9.4E-5 whcih is wrong.. So i assume that for the mass= 81 after a period of time the mass will decrease.. but how do you find the final amount of the fuel?

 

[Mindscrape]

You have to work in the mass somehow because with conservation you can see that p_initial = p_final, so

$$m_{p0}v_{p0} + M_{s0}V_{s0} = -(m_{p0}-m_{pejected})*v_{pf} + (M_{s0}-(m_{p0}-m_{pejected}))V_{sf}$$

where the terms on the left will be zero

As more ions are ejected, the spaceship will go faster.