A small 300 g ball and a small 600 g ball are connected by a 40-cm-long, 200 g rigid rod. a. How far is the center of mass from the 600 g ball?

Key Concepts

Center of Mass

The center of mass of a system is the point where the total mass of the system can be considered to be concentrated. It is calculated by taking the weighted average of the positions of all the masses in the system, where the weights are the masses themselves. For a system of discrete particles, the center of mass can be found using the formula: x_cm = (Σ(m_i * x_i)) / Σm_i, where m_i is the mass and x_i is the position of each particle.

Mass Distribution

Mass distribution refers to how mass is spread out in a system. In this problem, we have two balls of different masses connected by a rigid rod, which also has mass. Understanding how the masses are distributed along the rod is crucial for calculating the center of mass, as it affects the overall balance point of the system.

Coordinate System

A coordinate system is a framework used to define the position of points in space. In this problem, establishing a coordinate system (e.g., placing the 600 g ball at the origin) allows for easier calculations of distances and positions. By defining the positions of the masses relative to this system, we can accurately compute the center of mass and its distance from the specified ball.