Alpha Particle Elastic Collisions

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SUMMARY

The discussion focuses on the elastic collision between a proton and a stationary alpha particle (4He nucleus). The key equations used are conservation of momentum (Pi = Pf) and conservation of kinetic energy (Ki = Kf). The initial attempt to solve the problem involved incorrect substitutions, but the correct approach is to use the relationship v1 = v - 4v2 to derive the correct kinetic energy equation, leading to v^2 = v1^2 + 4v2^2. This allows for the calculation of the fraction of kinetic energy transferred to the alpha particle.

PREREQUISITES
  • Understanding of elastic collisions in physics
  • Familiarity with conservation laws (momentum and energy)
  • Basic algebra for manipulating equations
  • Knowledge of particle physics, specifically protons and alpha particles
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  • Study the principles of elastic and inelastic collisions in detail
  • Learn how to apply conservation of momentum and energy in particle collisions
  • Explore the concept of kinetic energy transfer in collisions
  • Investigate real-world applications of particle collisions in nuclear physics
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Students studying physics, particularly those focusing on mechanics and particle interactions, as well as educators looking for examples of elastic collisions in particle physics.

Workout
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Homework Statement



A proton strikes a stationary alpha particle (4He nucleus) head-on. Assuming the collision is completely elastic, what fraction of the proton’s kinetic energy is transferred to the alpha particle?

Homework Equations



Pi = Pf
Ki = Kf

The Attempt at a Solution


For Pi = Pf
mv = m1v1 + 4m2v2
cancel the m's out
v = v1 + 4v2

For Ki = Kf
1/2mv^2 = 1/2m1v1^2 + 1/2(4)m2v2^2
Cancel out the 1/2 and the m's

v^2 = v1^2 + 2v2^2

Now I'm lost.. can't substitute it into the equation, I feel like I got nowhere.

Help please.
 
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Workout said:

Homework Statement



A proton strikes a stationary alpha particle (4He nucleus) head-on. Assuming the collision is completely elastic, what fraction of the proton’s kinetic energy is transferred to the alpha particle?

Homework Equations



Pi = Pf
Ki = Kf

The Attempt at a Solution


For Pi = Pf
mv = m1v1 + 4m2v2
cancel the m's out
v = v1 + 4v2

For Ki = Kf
1/2mv^2 = 1/2m1v1^2 + 1/2(4)m2v2^2
Cancel out the 1/2 and the m's

v^2 = v1^2 + 2v2^2

Now I'm lost.. can't substitute it into the equation, I feel like I got nowhere.

Help please.
The second equation is not correct. It should be v^2 = v1^2 + 4v2^2
You can substitute v1=v-4v2 into it.


ehild
 

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