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10/14/09 - Center of Mass and Conservation of Momentum in Two Dimensions
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  | The center of mass of an object (also called the center of gravity) is the point where all the mass can be considered to be concentrated for certain purposes. The center of mass of a meter stick, for example would be its geometrical center (at the 0.50 m mark). If you support the center of mass, you can balance the whole meter stick. If you were to throw the meter stick through the air, its center of mass would move on a parabolic trajectory, just like a baseball, and the meter stick would rotate about its center of mass.
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  | We can find the center of mass of an object (or a group of objects) by multiplying each mass by its distance from a reference point, adding the values together and then dividing by the total mass:
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  | Find the center of mass of the three-mass system shown below:

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  | ycm = ((1.00kg)(0m) + (1.50kg)(0.25m) + (1.10kg)(0.125m))/(1.00kg+1.50kg+1.10kg) = 0.14m
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  | So the center of mass is at (0.44m, 0.14m).
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  | In the absence of an external force, the center of mass moves with constant velocity (constant speed in a straight line).
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  | In the presence of an external force, the center of mass moves as a point-object would move.
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  | Explosion in two dimensions
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  | In the absence of any external forces, momentum is conserved in both the x-direction and the y-direction.
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  | A 14-kg rock explodes, breaking into three pieces with the velocities shown. What is the speed of the 8 kg piece and what is its angle from the horizontal?

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  | Momentum in horizontal direction:
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  | Momentum in vertical direction: 0 = (4kg)(5m/s)sin(30°) - (8kg)(v)sin(θ)
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  | Elastic Collision in two dimensions
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  | Conservation of Kinetic Energy
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  | Solving 3 equations in 3 unknowns: v1, v2 and θ:
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  | Solving for v2 symbolically:
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  | Solving for v2 numerically:
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  | Cascade of collisions in one dimension
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  | Splashes, Craters and Chain Reachtions
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  | Read pp. 226-234 of the text.
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