Consider again the situation described in the last question, in which a sponge mounted on a low-friction cart collides with a rubber band. For the period between when the “sponge cart” first makes contact with the rubber band and when the sponge cart comes to a full stop, which one of the energy diagrams below best describes the interaction between the sponge cart and the rubber band?

The center of mass is given by:

∑mx/∑m

m is the mass of each object

x is the position of each object

We will assign x = 0m to the 18kg mass, therefore x = 6m for the 6kg mass.

∑mx/∑m = (18×0+6×6)/(18+6) = 1.5m

The center of mass is located 1.5m away from the 18kg mass.

The total moment of inertia of the system about the center of mass is given by:

I = ∑mr²

I is the moment of inertia

m is the mass of each object

r is the distance of each object from the center of mass

We know r = 1.5m for the 18kg mass and the rod is 6m long, therefore the 6kg mass must be r = 4.5m from the center of mass.

I = 18(1.5)² + 6(4.5)²

I = 162kg×m²