AMAT-2120. Fall 2004. Preparation to Final Exam.
Sample programming question 2:
Write a program that calculates the position of the Center of Mass of the given system

of point masses using the formulas below.
The values of x[i],y[i],m[i] should be provided by the user
(interactively, in the command line, or through an input file).

The number of point should either be supplied by the user or counted automatically.

> x[i],y[i],m[i]; Given

> N; Given or to be counted

> xc, yc; To find

Using a vector notation

> r[i]:=[x[i],y[i]]; position of point #i
R:=[xc, yc]; position of the center of mass

the result is given by

> R:=sum(m[i]*r[i],i=1..N)/M;

where M is the total mass of the system:

> M:=sum(m[i],i=1..N);

The above vector formula is equivalent to two scalar formulas:

> xc:=sum(m[i]*x[i],i=1..N)/M;
yc:=sum(m[i]*y[i],i=1..N)/M;