# Solving Proton Acceleration & Velocity: Conservation of Energy

• fubag
In summary, the conversation is discussing the conservation of energy and solving a problem involving a proton accelerating from rest and approaching a stationary heavy ion with the same charge. The problem involves finding the velocity and distance at different points in the motion. The correct method involves using the change in potential energy formula and setting it equal to the change in kinetic energy formula.
fubag
[SOLVED] Conservation of Energy

## Homework Statement

A proton (charge e, mass = 1.67 * 10^-27 kg) accelerates from rest by crossing a potential difference V = 3.00 V

a.) Find the velocity v_0 it acquires?

(Suppose this proton, having initial velocity v_0 from part (a), moves from very away directly towards a stationary heavy ion which is singly charged, i.e. having the same charge as the proton, +e.)

b.) Find the distance r_min between the proton and the ion at the moment of closest approach?

c.) Find velocity v of a proton when it is at a distance r = 2r_min from the ion

## Homework Equations

a = (q/m)E

V = kQ/r

V = E*d (parallel plate)

## The Attempt at a Solution

I am literally stuck for part a into determining what it could be, it seems something is missing in the problem.

Thanks!

fubag said:
I am literally stuck for part a into determining what it could be, it seems something is missing in the problem.

What is the work done on a charge q when it goes from a point with potential V1 to a point with potential V2?

work done is the change in potential energy so (V2 - V1)*q?

I was wondering could I just integrate the equation a = (q/m)E into v = (q/m)*V? because electric field is the derivative of potential difference?

fubag said:
work done is the change in potential energy so (V2 - V1)*q?

The change in KE is the work done. There's no need to integrate, since it is the potential difference which has been given.

I feel you should go through the basics once more by yourself.

I know change in potential energy = -Work

and that change in potential difference is the potential-energy change per unit charge...
so can't I just set Vq = U and then set that = (1/2)mv^2 and solve for v?

That's the correct way.

## 1. What is proton acceleration?

Proton acceleration refers to the process of increasing the speed or velocity of a proton using an external force, such as an electric field or magnetic field.

## 2. How is energy conserved during proton acceleration?

Energy is conserved during proton acceleration through the principle of conservation of energy. This means that the total energy of a system, including both kinetic and potential energy, remains constant throughout the acceleration process.

## 3. What factors affect the acceleration and velocity of a proton?

The acceleration and velocity of a proton can be affected by several factors, including the strength of the external force, the distance over which the force acts, and the initial energy of the proton.

## 4. How is proton acceleration used in scientific research?

Proton acceleration is used in a variety of scientific research fields, such as particle physics, nuclear medicine, and materials science. It allows scientists to study the behavior of protons at high speeds and energies, providing insights into the fundamental structure of matter.

## 5. What are some real-world applications of proton acceleration?

Proton acceleration has many practical applications, such as in cancer treatment through proton therapy, the production of radioisotopes for medical imaging, and the development of new materials for use in electronics and engineering. It also plays a crucial role in particle colliders, which are used to study the fundamental building blocks of the universe.

Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
6
Views
1K
Replies
6
Views
2K
Replies
17
Views
2K
• Electromagnetism
Replies
1
Views
1K
Replies
5
Views
2K
• Introductory Physics Homework Help
Replies
10
Views
779
• Introductory Physics Homework Help
Replies
4
Views
1K