Center of Mass

Animation 1

Animation 2

Animation 3


A spring that is attached to the ends of two carts. The spring is compressed when the two carts are placed next to each other on a low-friction track. The spring is released such that the two carts are “pushed” apart as shown in the animations (position is in meters and time is in seconds). In Animation 1, the system remains at the center of the animation, in Animation 2, the system moves to the right, and in Animation 3, the system moves to the left. The graphs depict the motion in the x-direction of the individual masses as a function of time.


Describe the motion of the center of mass in each animation.

Instructor Resources

Reference: See Giancoli-PA: 7-8, Giancoli-SE: 9-9.
Answer: Animation 1: The velocity of the center of mass is zero. Animation 2: The velocity of the center of mass is constant and positive (to the right). Animation 3: The velocity of the center of mass is constant and negative (to the left). Once these questions are answered, several other questions can be asked. For example, is energy conserved in any of the animations? Energy is of course conserved, but the actual calculation may be difficult depending on how students decide to undertake the calculation. It is apparent in the first animation that Vcm=0 and that the total energy is KEcm plus the energy stored in the spring at maximum compression/extension.
Script Author: Wolfgang Christian