Answer to Question #256803 in Physics for MCC

Question

Sam, Choi, Mich, Pia, and Sheen are on a 6’ x 4’ rectangular balsa. They are having trouble in keeping the balsa balanced as they are unaware of their center of mass. Find their center of mass, given the following: Sam is at 3 feet east, and 2 feet north of the balsa’s geometric center. She weighs 78 kg. 

Answer 1

Draw the balsa:

As we see, we only know the position of Sam, but we do not know his weight. Therefore, the canter of mass depends on other variables. On the whole, with the given system of coordinated, we have the following:

$$x_c=\frac{x_1m_1+x_2m_2+x_3m_3+x_4m_4+x_5m_5}{m_1+m_5+m_3+m_2+m_4},\\\space\\ y_c=\frac{y_1m_1+y_2m_2+y_3m_3+y_4m_4+y_5m_5}{m_1+m_5+m_3+m_2+m_4},$$

where

$y_i, x_i, m_i$ - y-, x-coordinate of each kid and their mass respectively. ince we do not have enough data, we can't get the numerical solution for the problem.