Calculating Vector Velocity in a Nuclear Reaction: Homework Problem

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Homework Help Overview

The problem involves calculating the magnitude of the velocity of a deuteron formed from a neutron and a proton colliding at different velocities in a nuclear reaction context. The neutron is moving at 1.0 × 107 m/s in the +x direction, while the proton is moving at 5.0 × 106 m/s in the +y direction. The assumption is made that both particles have the same mass.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss using the Pythagorean theorem to find the resultant velocity. Questions arise about how to properly account for momentum and velocity in the context of equal mass particles. There is also a consideration of the mass of the new particle formed.

Discussion Status

Some participants are exploring different interpretations of how to apply the Pythagorean theorem to the velocities involved. Others are questioning the relationship between momentum and velocity, particularly in the context of equal mass. A participant expresses gratitude for the assistance received, indicating some progress in understanding.

Contextual Notes

There is a mention of a discrepancy between the calculated velocity and the textbook answer, which may indicate a need for further clarification on the assumptions or methods used in the problem.

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Homework Statement



Consider a nuclear reaction in which a neutron traveling 1.0 × 107 m/s in the +x direction collides with a proton traveling 5.0 × 106 m/s in the +y direction. They combine at impact to form a new particle called a “deuteron.” What is the magnitude of the deuteron velocity? Assume for simplicity that the proton and neutron have the same mass.

Homework Equations



a2 + b2 = c2

The Attempt at a Solution



I would think you would just use the pythagorean theorem to solve the problem. When you do that you get 1.1 * 107 The textbook says the answer is 5.6 * 106
 
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bobsmith76 said:
I would think you would just use the pythagorean theorem to solve the problem.
You'd use the Pythagorean theorem to add the two momenta. But how would you solve for the new velocity?
 
But if their mass is the same then the momentum should equal the velocity. In the equation

p = mv

If m = 1, then p should equal v
 
bobsmith76 said:
But if their mass is the same then the momentum should equal the velocity. In the equation

p = mv

If m = 1, then p should equal v
If the mass of each original particle is '1' unit, what's the mass of the new combined particle?
 
Thanks, I got it. I really appreciate your help.
 

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