Help with conservation of kinetic energy and momentum

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Homework Statement



Alpha particle mass - 4amu
velocity alpha particle - 3.0x10^5m/s

197Au Nucleus mass - 197amu

Head-on elastic collision. Find the final velocity of both the particles

Homework Equations



Kinetic Energy conserved:
1/2m1v1i = 1/2m1v1f + 1/2m2v2f

Momentum Conserved:

m1v1i = m1v1f + m2v2f

The Attempt at a Solution




For Momentum:

4 x (3 x 10^5) = 4V1f + 197v2f
3 x 10^5 = V1f + 49.25v2f
V1f = 3 x 10^5 - 49.25v2f


For Kinetic Energy

4 x (3.0 x 10^5)2 = 4V1f2 + 197v2f2
3.6 x 1011 = 4V1f + 197v2f
9 x 1010 = V1f + 49.25v2f

Subbing in one for the other


9x 1010 = (300,000 - 49.25v2f)2 + 49.25v2f


The v2f and V1f values I get doesn't work out



Thanks in advance for your help.
 

Answers and Replies

  • #2
Redbelly98
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The Attempt at a Solution




For Momentum:

4 x (3 x 10^5) = 4V1f + 197v2f
3 x 10^5 = V1f + 49.25v2f
V1f = 3 x 10^5 - 49.25v2f


For Kinetic Energy

4 x (3.0 x 10^5)2 = 4V1f2 + 197v2f2
3.6 x 1011 = 4V1f + 197v2f
9 x 1010 = V1f + 49.25v2f

Subbing in one for the other


9x 1010 = (300,000 - 49.25v2f)2 + 49.25v2f
That last v2f is really v2f2, right?

The v2f and V1f values I get doesn't work out
What values do you get? It looks like the right approach.

p.s. Welcome to Physics Forums!
 

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