# What Was the Initial Speed of the Proton in a Collision?

• kristjan
In summary, the problem involves a moving proton hitting a stationary proton with a gap of 10(-13)m between them. The question is to find the initial speed of the moving proton, given the mass and charge of the protons. Using the equations for electric potential energy and kinetic energy, and assuming the target proton is held stationary, the initial speed is calculated to be 1.66*10(6) m/s. However, if the target proton is free to move and conservation of momentum and energy are considered, the initial speed is 2.35*10(6) m/s, which matches the book answer.
kristjan

## Homework Statement

The moving proton hits the second proton, which we consider to be stationary. In the moment of central strike gap between the protons is 10(-13)m. What was the initial speed of the moving proton? Proton mass is 1.67*10(-27)kg and charge 1.6*10(-19) C.

## Homework Equations

Electric potential energy U=kQq/r
Kinetic energy 1/2 mv2

## The Attempt at a Solution

kinetic energy is transformed into electric potential energy at the point of closest approach:
electric potential energy=kinetic energy of moving proton
From there I find initial speed of moving proton to be v=1.66*10(6) m/s, in book answer is 2.35*10(6) m/s

kristjan said:

## Homework Statement

The moving proton hits the second proton, which we consider to be stationary. In the moment of central strike gap between the protons is 10(-13)m. What was the initial speed of the moving proton? Proton mass is 1.67*10(-27)kg and charge 1.6*10(-19) C.

## Homework Equations

Electric potential energy U=kQq/r
Kinetic energy 1/2 mv2

## The Attempt at a Solution

kinetic energy is transformed into electric potential energy at the point of closest approach:
electric potential energy=kinetic energy of moving proton
From there I find initial speed of moving proton to be v=1.66*10(6) m/s, in book answer is 2.35*10(6) m/s
Perhaps, the other proton was stationary at the beginning, but free to move. Then momentum is conserved.

Remark by ehild above is right. If it is asumed that the target proton is (somehow) held stationary, then I am also getting the same answer that kristjan got. If you assume that the target proton is free to move, and that it is a 1-dimensional collision problem, using (non-relativistic) momentum and energy conservation, I get the book answer.

## 1. What is the initial speed of a proton?

The initial speed of a proton can vary depending on the source or experiment, but typically it ranges from 0.1-0.99 times the speed of light. This equates to speeds of approximately 30,000-297,000 kilometers per second.

## 2. How is the initial speed of a proton measured?

The initial speed of a proton can be measured using various techniques, such as particle accelerators or mass spectrometers. These methods allow scientists to accelerate protons to high speeds and then measure their velocity using specialized detectors.

## 3. What factors influence the initial speed of a proton?

The initial speed of a proton can be influenced by factors such as the energy of the source, the strength of the magnetic field, and the distance the proton has to travel. Additionally, the initial speed can also be affected by the mass and charge of the proton itself.

## 4. Why is the initial speed of a proton important to study?

The initial speed of a proton is important to study because it can provide valuable information about the properties of matter and the fundamental forces of the universe. Protons are also an essential component of atoms and play a crucial role in many physical and chemical processes.

## 5. Can the initial speed of a proton be changed?

Yes, the initial speed of a proton can be changed through various means, such as collisions with other particles or exposure to strong electric or magnetic fields. Scientists can also manipulate the initial speed of protons through advanced technologies like particle accelerators.

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