Center of Mass for Two Uncoupled Particles

• Central Forces 2023 (3 years)

  (Straightforward) Purpose: Discover that a system of two masses can be a central force system even when they are not interacting at all. Practice with center-of-mass coordinates.

  Consider two particles of equal mass \(m\). The forces on the particles are \(\vec F_1=0\) and \(\vec F_2=F_0\hat{x}\). If the particles are initially at rest at the origin, find the position, velocity, and acceleration of the center of mass as functions of time. Solve this problem in two ways,

  • with theorems about the center of mass motion,
  • without theorems about the center of mass motion.
  • Write a short description comparing the two solutions.