Assignment #8

Due: 11:00pm on Saturday, July 20, 2013

You will receive no credit for items you complete after the assignment is due. Grading Policy

Center of Mass and External Forces

Learning Goal:

Understand that, for many purposes, a system can be treated as a point-like particle with its mass concentrated at the center

of mass.

A complex system of objects, both point-like and extended ones, can often be treated as a point particle, located at the

system's center of mass. Such an approach can greatly simplify problem solving.

Before you use the center of mass approach, you should first understand the following terms:

System: Any collection of objects that are of interest to you in a particular situation. In many problems, you have

a certain freedom in choosing your system. Making a wise choice for the system is often the first step in solving

the problem efficiently.

Center of mass: The point that represents the "average" position of the entire mass of a system. The postion of

the center of mass can be expressed in terms of the position vectors of the particles as

The x coordinate of the center of mass can be expressed in terms of the x coordinates of the

particles as

Similarly, the y coordinate of the center of mass can be expressed.

Internal force: Any force that results from an interaction between the objects inside your system. As we will

show, the internal forces do not affect the motion of the system's center of mass.

External force: Any force acting on an object inside your system that results from an interaction with an object

outside your system.

Consider a system of two blocks that have masses and . Assume that the blocks are point-like particles and are

located along the x axis at the coordinates and as shown .

In this problem, the blocks can only move along the x axis.

Part A



∑



∑

(

)

∑ (

)

∑