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 15.7 g, 16.3 g, 22.7 g, and 22.1 g. At this very instant the x and y components of the mice's velocities are, respectively, (0.539 m/s, -0.271 m/s), (-0.943 m/s, -0.151 m/s), (0.517 m/s, 0.485 m/s), and (-0.713 m/s, 0.905 m/s).

Calculate the x and y components of Bryce's mice's total momentum, px and py.

Answer 1

Concepts and reason

The concept used to solve this question is linear momentum.

First, write expressions for the total momentum of Bryce’s mice’s in x and y-direction by using the concept of momentum. Later, determine total momentum of Bryce’s mice’s in x and y-direction by using the formulas of the total momentum.

Fundamentals

Linear momentum:

The linear momentum of an object is the product of its mass and speed in a specific direction. It is generally denoted by letter p. The unit of momentum is.

The expression of linear momentum or momentum is:

Here, is the mass of an object and is the speed of the object.

The total momentum of Bryce’s mice’s in the x-direction can be expressed as,

…… (1)

Here, is total momentum of Bryce’s mice’s in the x-direction, are the recorded masses and are the speed of recorded masses in the x-direction.

The total momentum of Bryce’s mice’s in the y-direction can be expressed as,

…… (2)

Here, is total momentum of Bryce’s mice’s in the y-direction, and are the speed of recorded masses in the y-direction.

Substitute for, for, for, for, for, for, for, for in equation (1).

Substitute for, for, for, for, for, for, for, for in equation (2).

Ans:

The total momentum of Bryce’s mice’s in x and y-direction is and.