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[solved] resulting velocity of 2 particles
conservation of momentum
[tex]m_Av_A'=m_Bv_B'[/tex]
[tex]v_A'=\frac{m_B}{m_A}v_B'[/tex]
conservation of energy
[tex]V=\frac{1}{2}m_A(v_A')^2+\frac{1}{2}m_B(v_B')^2=\frac{1}{2}m_A\left(\frac{m_B}{m_A}v_B'\right)^2+\frac{1}{2}m_B(v_B')^2[/tex]
[tex]v_B'=\sqrt{\frac{2m_AV}{m_B(m_A+m_B)}}[/tex]
[tex]m_A=0.9Kg[/tex]
[tex]m_B=1.35Kg[/tex]
[tex]V=1.35Nm[/tex]
[tex]v_B'=\sqrt{\frac{2\cdot0.9\cdot1.35}{1.35(0.9+1.35)}}=\sqrt{0.8}\approx{0.8944[m/s]}[/tex]
[tex]v_A'=\frac{1.35}{0.9}\cdot0.8944=1.3416[m/s][/tex]
from the law of cosines
[tex]v_B=\sqrt{6^2+0.8944^2-2\cdot6\cdot0.8944\cdot\cos{60^o}}\approx5.607[m/s][/tex]
from the law of sines
[tex]\sin{\beta}=\frac{\sin{60^o}\cdot0.8944}{5.607}\approx0.1381[/tex]
[tex]\beta\approx7.94^o[/tex]
As you can see that result is totally different from the solution given by my teacher. I also get different results for the other velocity. So either my calculations are incorrect or my teacher gave us wrong results. I'll be grateful for any help, thank you.
Homework Statement
Homework Equations
conservation of momentum
[tex]m_Av_A'=m_Bv_B'[/tex]
[tex]v_A'=\frac{m_B}{m_A}v_B'[/tex]
conservation of energy
[tex]V=\frac{1}{2}m_A(v_A')^2+\frac{1}{2}m_B(v_B')^2=\frac{1}{2}m_A\left(\frac{m_B}{m_A}v_B'\right)^2+\frac{1}{2}m_B(v_B')^2[/tex]
[tex]v_B'=\sqrt{\frac{2m_AV}{m_B(m_A+m_B)}}[/tex]
The Attempt at a Solution
[tex]m_A=0.9Kg[/tex]
[tex]m_B=1.35Kg[/tex]
[tex]V=1.35Nm[/tex]
[tex]v_B'=\sqrt{\frac{2\cdot0.9\cdot1.35}{1.35(0.9+1.35)}}=\sqrt{0.8}\approx{0.8944[m/s]}[/tex]
[tex]v_A'=\frac{1.35}{0.9}\cdot0.8944=1.3416[m/s][/tex]
from the law of cosines
[tex]v_B=\sqrt{6^2+0.8944^2-2\cdot6\cdot0.8944\cdot\cos{60^o}}\approx5.607[m/s][/tex]
from the law of sines
[tex]\sin{\beta}=\frac{\sin{60^o}\cdot0.8944}{5.607}\approx0.1381[/tex]
[tex]\beta\approx7.94^o[/tex]
As you can see that result is totally different from the solution given by my teacher. I also get different results for the other velocity. So either my calculations are incorrect or my teacher gave us wrong results. I'll be grateful for any help, thank you.
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