This is a follow-up of question http://www.experts-exchange.com/Other/Math_Science/Q_26846773.html
The 4 bodies have equal mass (m) and same initial speeds. Three of the bodies, known as B, C, and D will be treated as one system. The fourth body, A, is the second system. My goal is to derive an effective single point entity that represents the B-C-D system in order to compute the force on A due to the B-C-D system.
Their initial configuration is a square (whose diagonals have a length 2r), and their velocities are shown here:
Vb^ . .
| . .
\ / |
\ / v Vd
In order to determine the force acting on A due to the B-C-D system, I thought I could treat the B-C-D system as an effective single entity having mass equal to 3m and whose location is the CM of B-C-D.
If this is an incorrect assumption, could you provide me with the correct way to derive an effective single entity that acts on A.
Using this assumption, I determined the CM to be 1/3 the distance on the line from C to the other system, A. (As expected, the CM of the triangle is on a bisector of the angle BCD.) Since ABCD is a square, angle BCD = 90 degrees). Since the diagonal length is 2r, then the distance from A to the CM is (2/3)(2r) = (4/3)r.
But when I compute the force on A by this effective single 3m entity at the CM, the force on A is different than the force in the previous related question. I am looking for consistency.
Maybe arithmetic or algebra is wrong, or maybe my assumption is wrong.