Bryce, a mouse lover, keeps his four pet mice in a roomy cage, where they spend much of their spare time (when they are not sleeping or eating) joyfully scampering about on the cage's floor. Bryce tracks his mice's health diligently and just now recorded their masses as 14.5 g,14.5 g, 18.3 g,18.3 g, 13.3 g,13.3 g, and 10.5 g.10.5 g. At this very instant, the xx ‑ and yy ‑components of the mice's velocities are, respectively, (0.127 m/s, −0.907 m/s),(0.127 m/s, −0.907 m/s), (−0.781 m/s, −0.103 m/s),(−0.781 m/s, −0.103 m/s), (0.867 m/s, 0.471 m/s),(0.867 m/s, 0.471 m/s), and (−0.213 m/s, 0.851 m/s).(−0.213 m/s, 0.851 m/s). Calculate the xx ‑ and yy ‑components of Bryce's mice's total momentum, pxpx and py.

Accepted Solution

Answer:[tex]P_{x}=-3.1562 g*m/s[/tex][tex]P_{y}= 0.1634 g*m/s[/tex]Step-by-step explanation:The x-component and y-component of the total momentum is given by:[tex]P_{x}=m_{1}v_{x1}+m_{2}v_{x2} + m_{3}v_{x3}+m_{4}v_{x4}\\P_{y}=m_{1}v_{y1}+m_{2}v_{y2} + m_{3}v_{y3}+m_{4}v_{y4}\\[/tex]Substituting values:[tex]P_{x}=14.5g(0.127m/s) + 18.3g(-0.781m/s) + 13.3g(0.867m/s)+10.5g(-0.213m/s)\\P_{x}=-3.1562 g*m/s[/tex][tex]P_{y}=14.5g(-0.907m/s) + 18.3g(-0.103m/s) + 13.3g(0.471m/s)+10.5g(0.851m/s)\\P_{y}= 0.1634 g*m/s[/tex]