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AP Physics Center of Mass

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**Why does the high jumper do the “Fosbury flop?”**

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**Center of Mass of a system**

When the net external force on a system is zero, the motion of the CM of that system will not change (law of inertia) M = m1 + m2 + … = Smi

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A penguin stands at the left edge of a uniform sled of length L, which lies on frictionless ice. The sled and penguin have equal masses. (a) Where is the center of mass of the sled? (b) How far and in what direction is the center of the sled from the center of mass of the sled–penguin system? The penguin then waddles to the right edge of the sled, and the sled slides on the ice. (c) Does the center of mass of the sled–penguin system move leftward, rightward, or not at all? (d) Now how far and in what direction is the center of the sled from the center of mass of the sled–penguin system? (e) How far does the penguin move relative to the sled? Relative to the center of mass of the sled–penguin system, how far does (f) the center of the sled move and (g) the penguin move?

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A right cylindrical can with mass M, height H, and uniform density is initially filled with soda of mass m. We punch small holes in the top and bottom to drain the soda; we then consider the height h of the center of mass of the can and any soda within it. What is h (a) initially and (b) when all the soda has drained? (c) What happens to h during the draining of the soda? (d) If x is the height of the remaining soda at any given instant, find x (in terms of M, H, and m) when the center of mass reaches its lowest point.

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