Alpha Particle Elastic Collisions

[Workout]

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.

 

[ehild]

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