Here is the question:
A thin triangular plate of uniform density and thickness has vertices at v1 = (0,1), v2 = (8,1), and v3 =(2,4), and the mass of the plate is 3g.
a. Find the (x,y)-coordinates of the center of mass of the plate. This "balance point" of the plate coincides with the center of mass of a system consisting of three 1 gram point masses located at the vertices of the plate.
b. Determine how to distribute an additional mass of 6 g at the three vertices of the plate to move the balance point of the plate to (2,2). [Hint: let w1, w2, and w3 denote the masses added at the three vertices, so that w1 + w2 + w3 = 6.]
I got 'a.' right, but I am confused about what to do with 'b.'. I tried doing this : (1/9)[v1 v2 v3], and then i created an augmented matrix out of the result by placing the (2,2) as the last column. But I had more variables than rows and I didn't know how to solve it.
A thin triangular plate of uniform density and thickness has vertices at v1 = (0,1), v2 = (8,1), and v3 =(2,4), and the mass of the plate is 3g.
a. Find the (x,y)-coordinates of the center of mass of the plate. This "balance point" of the plate coincides with the center of mass of a system consisting of three 1 gram point masses located at the vertices of the plate.
b. Determine how to distribute an additional mass of 6 g at the three vertices of the plate to move the balance point of the plate to (2,2). [Hint: let w1, w2, and w3 denote the masses added at the three vertices, so that w1 + w2 + w3 = 6.]
I got 'a.' right, but I am confused about what to do with 'b.'. I tried doing this : (1/9)[v1 v2 v3], and then i created an augmented matrix out of the result by placing the (2,2) as the last column. But I had more variables than rows and I didn't know how to solve it.