# Problem: Consider a system consisting of three particles with velocities given in terms of a 3D coordinate system (x, y, and z axes): 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 What Is the total kinetic energy of thls system? Ktot = _____ J

###### FREE Expert Solution

Kinetic energy:

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

3D vector magnitude:

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

Ktot = K1 + K2 + K3

K1 = (1/2)m1v12 = (1/2)(m1)(v1x2 + v1y2 + v1z2) = (1/2)(2)((10)2 + (-5)2 + (12)2) = 269 J

91% (208 ratings) ###### Problem Details

Consider a system consisting of three particles with velocities given in terms of a 3D coordinate system (x, y, and z axes):

m1 = 2 kg, v1  = < 10, -5, 12 > m/s

m= 9 kg, v2 = < -14, 3, -3>m/s

m= 2 kg, v3 = < -23, 37, 20 > m/s

What Is the total kinetic energy of thls system?

Ktot = _____ J

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