Question

Three 81.6 g masses are connected in a triangular shape by massless rigid wires as shown in the first image (which is not drawn to scale). The coordinates of each mass are given in centimeters. Mass A is located at (0,0) , mass B is at (12.2,22.5) , and mass C is at (21.3,13.4) . Find the ? - and ? ‑coordinates of the center of mass of the triangular object. A graph has a vertical Y axis and a horizontal X axis. Three masses are shown. Mass A is located at (0,0), mass B is at (12.2,22.5), and mass C is at (21.3,13.4). ?cm= cm ?cm= cm Two more 81.6 g masses are connected by a straight piece of wire and affixed to the original configuration as shown. The coordinates of mass D are (0,−27.0) and the coordinates of mass E are (0,27.0) . Find the ? - and ? ‑coordinates of the new center of mass of the combined object. A graph has a vertical Y axis and a horizontal X axis. Five masses are shown. Mass A is located at (0,0), mass B is at (12.2,22.5), mass C is at (21.3,13.4), mass D is at (0, -27.0), and mass E is at (0, 27.0). ?cm= cm ?cm= cm

Answer 1

Center of mass X (Y) can be calculated by using the following formula

Here, we shall be using subscripts 1,2 and 3 for A, B and C points , respectively. masses are same m1=m2=m3=m. The above equations reduces to

Similarly Y can be calculated as

The x and y coordinates of center of mass are X= 11.17 cm and Y=11.96 cm.

Now we calculate by including points D and E as well. In this case Eq. (1) and Eq. (2) takes the following form

.Here, we are using subscripts 4 and 5 for D and E, respectively. Again the mass is same so replacing all masses by m and solving for center of mass for the entire system

Similarly, Y can be given as

Now the center of mass shifted to X =6.7 cm and Y= 7.18 cm