PROBLEM 30E

Let v be the center of mass of a system of point masses located at v1, … , vk as in Exercise 29. Is v in Span {v1, … , vk}? Explain.

Exercise 29:

Let v1, … , vk be points in ℝ3 and suppose that for j= 1, … ,k an object with mass mj is located at point vj . Physicists call such objects point masses. The total mass of the system of point masses is

The center of gravity (or center of mass) of the system is

Compute the center of gravity of the system consisting of the following point masses (see the figure):

Solution :

Step 1 :

Let v1,...,Vk be points in ℝ3 and suppose that for j = 1,..., k an object with mass mj is located at point vj. Physicists call such objects point masses. The total mass of the system of point masses is

m = ml + m2 +m3...... + mk