Question

Bryce, a mouse lover, keeps his four pet mice in a roomy cage, where they spend much of their spare timeâwhen they\'re not sleeping or eatingâjoyfully scampering about on the cage\'s floor. bryce tracks his mice\'s health diligently and just now recorded their masses as 0.0141 kg, 0.0101 kg, 0.0207 kg, and 0.0169 kg. at this very instant the x and y components of the mice\'s velocities are, respectively, (0.189 m/s, -0.841 m/s), (-0.211 m/s, -0.399 m/s), (0.513 m/s, 0.239 m/s), and (-0.685 m/s, 0.719 m/s). calculate the x and y components of bryce\'s mice\'s total momentum, px and py.

Answer 1

The x component of the mices' total momentum is the algebraic sum of the momenta  of the 4 mice on the x-axis:
$p_x = m_1 v_{x1}+m_2 v_{x2}+m_3 v_{x3}+m_4 v_{x4}=$
$= (0.0141 kg)(0.189 m/s)+(0.0101 kg)(-0.211 m/s)+$
$+(0.0207 kg)(0.513 m/s)+(0.0169 kg)(-0.685 m/s)=-4.24 \cdot 10^{-4}kg m/s$

Similarly the y component of the mices' total momentum is the algebraic sum of the momenta  of the 4 mice on the y-axis:
$p_y = m_1 v_{y1}+m_2 v_{y2}+m_3 v_{y3}+m_4 v_{y4}=$
$= (0.0141 kg)(-0.841 m/s)+(0.0101 kg)(-0.399 m/s)+$
$+(0.0207 kg)(0.239 m/s)+(0.0169 kg)(0.719 m/s)=1.21 \cdot 10^{-3}kg m/s$