Point-masses mi are located on the x-axis as shown. Find the moment M of the system about the origin and the center of mass x.

Question

m=?

x=?

number line

9 11

<0---(10)------(30)------>

What is the exact answer for this problem? or help setting this one up?

Answer 1

Center of mass is basically a weighted average. Calculus likes to view things as functions, so with y as a function of x, the weighted average is the sum of each x * y (with x being the location and y being the mass at that location), divided by the total mass M:

(∑xy) / M

With this I get an answer (21) very close to yours (21.5), which makes it sound like an arithmetic error:

(9*10 + 11*30)/20 = 21