I'm having trouble approaching the following problem:
A research group is designing a device which will separate fast moving ions from slow moving ones. To do this, the ions are brought into the device in a narrow beam, so that all of the ions are going in the same direction. The ion beam then passes between two parallel metal plates, separated by 3 cm from each other. Each plate is 5.0 cm long and 4.0 cm wide. A high voltage is applied to the plates causing the ions passing between them to have a constant acceleration directly toward one of the plates and away from the other plate. Before the ions enter the gap between the plates, they are going directly toward the center of the gap, parallel to the surface of the plates. After the ions leave the gap between the plates, they are no longer accelerated during the 50 cm journey to the ion detector. I need to find the acceleration required to separate ions with a velocity 100 m/sec from those in the beam going 1000 m/sec by 2.0 cm.
What should I do next?
I think the equations that I need to use for this problem are as follows:
1)Xfinal = Xinitial + Vinitialt + .5*a*t2
2)Vfinal = Vinitial + a*t
3)Vfinal2 = Vinitial2 + 2aΔX
The Attempt at a Solution
After I put some thought to this, I came to the conclusion that 2.0 cm is going to be the ΔY. The time that takes both kinds of ions to spend between the plates is:
For faster ions: t = .05m / 1000 m/sec = 5.0 * 10-5 sec
For slower ions: t = .05 m / 100 m/sec = 5.0 * 10-4 sec
What do I do next?