Calculating Acceleration of Ions in 2D Motion for Cancer Tumor Treatment

[StephenDoty]

You are asked to consult for the city's research hospital, where a group of doctors is investigating the bombardment of cancer tumors with high-energy ions. The ions are fired directly toward the center of the tumor at speeds of 5.50 times 10^6. To cover the entire tumor area, the ions are deflected sideways by passing them between two charged metal plates that accelerate the ions perpendicular to the direction of their initial motion. The acceleration region is 5.0 cm long, and the ends of the acceleration plates are 1.5 m from the patient. What acceleration is required to move an ion 2.0 cm to one side?

Do I use the given velocity as the x componet of the velocity??
Thus giving V0y/v0x=.02m/1.5m
V0y/5.50E6=.02m/1.5m
for the large triangle

then for the acceleration
I use .05m for the s, 0 for V0, but for Vf what do I use to complete Vf^2=v0^2 +2as to find the acceleration??

Thanks
Stephen

 

[StephenDoty]

forgot the picture

 

[awvvu]

I wouldn't try to find V_f. Split the problem into two parts: one in which there's acceleration, and one in which it's traveling at constant velocity. Combine these two together and you should be able to solve for a. You mostly need to worry about movement along the y-axis only, but the x-axis velocity affects the time the ion spends traveling. It's never changed though.

 

[StephenDoty]

where do I split it off?
at the acceleration plates?
so v0=0 and vf=5.5E^6 and s=.05m??

And then what would I do for the second part??
make v0=5.5E^6?

 

[awvvu]

Split it off when there is no longer no acceleration. After the plates, it moves in a straight line.

Find the time the particle spends inside the plates and the time it spends moving in a straight line. So, therefore you'll know the initial velocity for when it starts moving in a straight line.