- #1
Amrator
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Homework Statement
Ok, so this question is not really a homework problem but just something I'm trying to solve for fun and to improve my problem solving skills.
You must 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 copper plates. Each plate is 5.0 cm long, 4.0 cm wide, and the two plates are separated by 3.0 cm. 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. You boss asks you to calculate the magnitude of acceleration between the plates necessary to separate ions with a velocity of 100 m/s from those in the beam going 1000 m/s by 2.0 cm when they hit the ion detector 50 cm away. Before the ions enter the gap between the plates, they are going directly toward the center of the gap parallel to the surfaces of the plates. After the ions leave the gap between the plates, they are no longer accelerated during the remaining 50 cm to the ion detector. You look at the ion detector and find its face be circle with a radius of 7 cm.
Homework Equations
##X_f = X_0 + V_0t + (1/2)at^2##
The Attempt at a Solution
Ignore the 48.04 cm. I realize that's wrong. Same thing with the 2.3. That shouldn't be there.
So I figured that a lot of the information they gave was irrelevent, such as the dimensions of the plates and the radius of the detector. I used Pythagorean theorem to find the velocity of ##X_{2c}## after it left the plates,
##X_{2c} = \sqrt(50^2 + 2^2)##
I just don't know where to go from here. I've been staring at this problem for hours.