What Acceleration Is Needed for Ion Deflection in Cancer Treatment?

[monkey888888]

Homework Statement

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 4.5 . 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 long, and the ends of the acceleration plates are 1.5 from the patient. What acceleration is required to move an ion 2.0 to one side?

In one contest at the county fair, a spring-loaded plunger launches a ball at a speed of 3.90 from one corner of a smooth, flat board that is tilted up at a 20 angle. To win, you must make the ball hit a small target at the adjacent corner, 2.48 away. At what angle should you tilt the ball launcher?

 

[tiny-tim]

Welcome to PF!

Hi monkey888888! Welcome to PF!

Show us what you've tried, and where you're stuck, and then we'll know how to help.

 

[baba89]

I would approach this problem by first understanding the principles of kinematics in two dimensions. This involves analyzing the motion of objects in two dimensions, taking into account both the horizontal and vertical components of their motion.

In the first scenario, we are dealing with the motion of high-energy ions being deflected by charged metal plates. To determine the required acceleration, we can use the equation for displacement in the x-direction, which is given by:

x = x0 + v0x*t + (1/2)*ax*t^2

Where x is the final displacement, x0 is the initial displacement, v0x is the initial velocity in the x-direction, t is time, and ax is the acceleration in the x-direction.

In this case, we know the initial velocity (4.5 m/s) and the final displacement (2.0 m). We also know the length of the acceleration region (5.0 m) and the distance from the patient (1.5 m). By rearranging the equation and solving for ax, we can determine the required acceleration to move an ion 2.0 m to one side.

In the second scenario, we are dealing with the motion of a ball being launched from a spring-loaded plunger. To determine the required angle of the board, we can use the equation for range of projectile motion, which is given by:

R = (v0^2*sin2θ)/g

Where R is the range, v0 is the initial velocity, θ is the angle of the board, and g is the acceleration due to gravity.

In this case, we know the initial velocity (3.90 m/s) and the distance to the target (2.48 m). By rearranging the equation and solving for θ, we can determine the required angle to tilt the board in order to hit the target.

In both scenarios, it is important to consider any potential sources of error and to perform multiple trials to ensure accurate results. Additionally, it may be helpful to consult with other experts in the field to get a better understanding of the specific parameters and variables involved in these experiments.