Question

John's mass is 86 kg, and Barbara's is 55 kg. He is standing on the x axis at xJ = +9.0 m, while she is standing on the x axis at xB = +2.0 m. They switch positions. How far and in which direction does their center of mass move as a result of the switch?

Answer 1

initial position of the center of mass

$Mr_{icm}=m_{j}\cdot r_{j}\dotplus m_{b}\cdot r_{b}\Rightarrow r_{icm}=\frac{m_{j}\cdot r_{j}\dotplus m_{b}\cdot r_{b}}{M}=\frac{86kg\cdot 9m\dotplus 55kg\cdot 2m}{86kg\dotplus 55kg}=6,3m$

reversing the position

$Mr_{fcm}=m_{j}\cdot r_{j}\dotplus m_{b}\cdot r_{b}\Rightarrow r_{fcm}=\frac{m_{j}\cdot r_{j}\dotplus m_{b}\cdot r_{b}}{M}=\frac{86kg\cdot 2m\dotplus 55kg\cdot 9m}{86kg\dotplus 55kg}=4,7m$

displacement of the center of mass .

$\Delta r_{cm}=r_{fcm}-r_{icm}=4,7m-6,3m=-1,6m$}

1,6metros moves leftwards