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Center-of-Mass

Center-of-Mass. For a meter stick 100cm long, its center of mass would be in the middle at the 50cm point. CM. 0 50 100.

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Center-of-Mass

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  1. Center-of-Mass For a meter stick 100cm long, its center of mass would be in the middle at the 50cm point. CM 0 50 100 When we think about objects in motion, we automatically use that object’s Center-of-Mass in our calculations. But what is the Center-of-Mass? If we say an object has evenly distributed mass, we mean that all its mass is evenly distributed aboutasinglepoint. That point is its Center-of-Mass. If an object’s mass is NOT evenly distributed, we can still find the single point where as much mass is to one side as the other. That point is its Center-of-Mass. For a wrench 100cm long, its center of mass would NOT be in the middle at the 50cm point. The Center-of-Mass is shifted closer to the more massive side. CM

  2. An object’s Center-of-Mass can be shifted horizontally when its mass is not distributed evenly. An object’s Center-of-Mass can ALSO be shifted vertically when its mass is not evenly distributed. Example: A forklift’s horizontal Center-of-Mass is normally about here: But if there is a mass on the forks, then the Center-of-Mass is shifted forward: CM CM A forklift’s vertical Center-of-Mass is normally about here: CM And if the forks are raised, the Center-of-Mass will rise also: CM Raising the Center-of-Mass makes an object UNSTABLE !

  3. How to find the Center of Mass: It’s easy if the object’s mass is evenly distributed. Consider a common brick 20cm long, 10cm high and 12 cm deep. Its mass is evenly distributed. In the x direction, all its mass is centered at 10cm (half way) In the y direction, its mass would be centered at 5cm (half way) In the z direction, its mass would be centered at 6cm (halfway) y z The Center-of-Mass is half-way in each axis. The CM is at the coordinate: (10, 5, 6) 10 cm CMy 12cm 0 20 cm x CMx CMz

  4. How to find the Center of Mass: It’s NOT as easy if the object’s mass is unevenly distributed. Distance from a reference point (m1*d1) + (m2*d2) + (m3*d3) + . . . We need to use an equation: CM = m1 + m2+ m3 + . . . Each object’s mass A forklift will pick up a 1m long pallet loaded with three boxes of different masses. The boxes are centered at 0.2m, 0.5m, and 0.75m away from the left edge of the pallet. Find the Center-of-Mass. (10kg*0.2m) + (30kg*0.5m) + (60kg*0.75m) CM = 10kg + 30kg+ 60kg 60 kg CM = 0.62m from the left edge 30 kg 10kg The CM is not in the middle (0.5m) because the mass is not evenly distributed. It is more toward the more massive boxes. 0.2m 0.5m 0.75m

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