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# Problem: Consider a system consisting of three particles: m1 = 2 kg, v1  &lt; 10, -5, 12 &gt; m/s m2 = 9 kg, v2 &lt;- 14, 3, -3&gt;m/s m3 = 2 kg, v3 &lt;- 23, 37, 20 &gt; m/s vCM = (-11.7, 7.0, 2.85) m/sWhat Is the translational kinetic energy of this system? Ktrans = J

###### FREE Expert Solution

Kinetic energy:

$\overline{){\mathbf{K}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{\mathbf{v}}}^{{\mathbf{2}}}}$

3D vector magnitude:

$\overline{){\mathbf{|}}{\mathbf{v}}{{\mathbf{|}}}^{{\mathbf{2}}}{\mathbf{=}}{{{\mathbf{v}}}_{{\mathbf{x}}}}^{{\mathbf{2}}}{\mathbf{+}}{{{\mathbf{v}}}_{{\mathbf{y}}}}^{{\mathbf{2}}}{\mathbf{+}}{{{\mathbf{v}}}_{{\mathbf{z}}}}^{{\mathbf{2}}}}$

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###### Problem Details

Consider a system consisting of three particles:

m1 = 2 kg, v1  < 10, -5, 12 > m/s

m= 9 kg, v<- 14, 3, -3>m/s

m= 2 kg, v<- 23, 37, 20 > m/s

vCM = (-11.7, 7.0, 2.85) m/s

What Is the translational kinetic energy of this system?

Ktrans = J

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