(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Alpha particle mass - 4amu

velocity alpha particle - 3.0x10^5m/s

^{197}Au Nucleus mass - 197amu

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

2. Relevant equations

Kinetic Energy conserved:

1/2m_{1}v_{1i}= 1/2m_{1}v_{1f}+ 1/2m_{2}v_{2f}

Momentum Conserved:

m_{1}v_{1i}= m_{1}v_{1f }+ m_{2}v_{2f}

3. The attempt at a solution

For Momentum:

4 x (3 x 10^5) = 4V_{1f}+ 197v_{2f}

3 x 10^5 = V_{1f}+ 49.25v_{2f}

V_{1f}= 3 x 10^5 - 49.25v_{2f}

For Kinetic Energy

4 x (3.0 x 10^5)^{2}= 4V_{1f}^{2}+ 197v_{2f}^{2}

3.6 x 10^{11}= 4V_{1f}+ 197v_{2f}

9 x 10^{10}= V_{1f}+ 49.25v_{2f}

Subbing in one for the other

9x 10^{10}= (300,000 - 49.25v_{2f})^{2}+ 49.25v_{2f}

The v_{2f}and V_{1f}values I get doesn't work out

Thanks in advance for your help.

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# Homework Help: Help with conservation of kinetic energy and momentum

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