Center of Mass
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.
the motion of the center of mass in each animation.
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