Imagine you have two identical cans of pop (same brand, same size can, etc.); wi

Question

Imagine you have two identical cans of pop (same brand, same size can, etc.); with the exception that one frozen and one is not. You place them at the same vertical height at the top of an incline plane and release them simultaneously, from rest, allowing them to race down the incline. Describe the velocity of the respective cans as they reach the bottom of the incline; in effect, qualitatively justifying which can of pop will win the race.......or if there will be a tie.

how would you figure out the moments of inertia for the different cans? and how would you qulitatively expalin that?

Explanation / Answer

Assuming the objects do not slip as they roll down the inclined plane. acceleration = g*sin(theta)/[1+{I/(M*R^2)}] The can which is not frozen will have larger moment of inertia as compared to the frozen one because during rolling, the liquid inside the can will have a tendency to stick to the walls of the can, thereby increasing the distance between the net mass of liquid and the axis of the can. And, as acceleration of a rolling object down an incline is inversely proportional to its moment of inertia, the acceleration of the frozen can will be greater and so, it will win the race.

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