Question

Bryce, a mouse lover, keeps his four pet mice in a roomy cage, where they spend much of their spare time, when they're 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 0.0173 0.0173 kg, 0.0233 0.0233 kg, 0.0145 0.0145 kg, and 0.0199 0.0199 kg. At this very instant, the x ‑ x‑ and y ‑ y‑ components of the mice's velocities are, respectively, ( 0.899 m/s , − 0.757 m/s ) (0.899 m/s,−0.757 m/s) , ( − 0.655 m/s , − 0.957 m/s ) (−0.655 m/s,−0.957 m/s) , ( 0.785 m/s , 0.731 m/s ) (0.785 m/s,0.731 m/s) , and ( − 0.837 m/s , 0.111 m/s ) (−0.837 m/s,0.111 m/s) . Calculate the x ‑ x‑ and y ‑ y‑ components of Bryce's mice's total momentum, p x px and p y py .

Answer 1

Answer:

The momentum of the mice, presented in the form (px, py) are given respectively

(0.01555 kgm/s, -0.01310 kgm/s)

(-0.01526 kgm/s, -0.02230 kgm/s)

(0.01138 kgm/s, 0.01060 kgm/s)

(-0.01666 kgm/s, 0.00221 kgm/s)

Explanation:

Momentum is simply given as the product of mass and velocity

The masses of the mice include

0.0173 kg, 0.0233 kg, 0.0145 kg, and 0.0199 kg.

And the corresponding x and y components of the mice velocities at the instant is given as

(0.899 m/s,−0.757 m/s), (−0.655 m/s,−0.957 m/s), (0.785 m/s,0.731 m/s) , and (−0.837 m/s,0.111 m/s)

Hence the x and y components of the mice's total momentum is given as

0.0173 (0.899, −0.757) = (0.0155527, -0.0130961) kgm/s

= (0.01555 kgm/s, -0.01310 kgm/s)

0.0233 (−0.655,−0.957) = (-0.0152615, -0.0222981) kgm/s

= (-0.01526 kgm/s, -0.02230 kgm/s)

0.0145 (0.785, 0.731) = (0.0113825, 0.0105995) kgm/s

= (0.01138 kgm/s, 0.01060 kgm/s)

0.0199 (−0.837, 0.111) = (-0.0166563, 0.0022089) kgm/s

= (-0.01666 kgm/s, 0.00221 kgm/s)

Hope this Helps!!!