Center of Mass.notebook December 16, 2015 Up to this point, we have simplified situations by describing an object as a point particle. In actuality, different parts of objects behave differently. Ex: A diver. In figure (a), the motion is represented a point particle. In figure (b), a more realistic display of the motion is occuring. Notice the black dot at the waist of the diver. This dot represents the center of mass which travels the same expected path as an idealized object in each figure. Center of Mass (CM) the single point that moves in the same path that a particle would move if subjected to the same net force. Logic behind this idea: Consider any object as being made up of tiny distinct particles of individual mass and position. So each particle with its own unique mass is some unique distance away from a reference point. If we continually add all these particles together we will get the entire mass of the object and the total length. The distribution of these different masses at different positions will affect the location of the center of mass, the average position of all the particles of mass that make up an object. The center of gravity (CG) is the same point if the object is in a uniform gravitational field Let's consider the figure , a system of two particles, mA and mB, that are located at positions xA and xB away from the origin. a) If mA >mB, predict where xCM is located. b) If mA <mB, predict where xCM is located. c) If mA =mB, predict where xCM is located. To calculate x CM, use the following equation. xCM = mA xA + mB xB / (mA + mB) Practice: Solve if xA = 10 cm, mA = 4 kg, xB = 40 cm, mB = 2 kg The more particles in a system, the more terms added to the top and bottom of the previous equation. The general form follows: xCM = Σ(m x) / Σm If there is more than one dimension, then the location of the center of mass for each direction (X, Y & Z) should be calculated and the location described using each. The center of mass can be found experimentally by balancing the object at one point.
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Center of Mass.notebook December 16, 2015
Up to this point, we have simplified situations by describing an object as a point particle. In actuality, different parts of objects behave differently.
Ex: A diver. In figure (a), the motion is represented a point particle. In figure (b), a more realistic display of the motion is occuring.
Notice the black dot at the waist of the diver. This dot represents the center of mass which travels the same expected path as an idealized object in each figure.
Center of Mass (CM) the single point that moves in the same path that a particle would move if subjected to the same net force.
Logic behind this idea:
Consider any object as being made up of tiny distinct particles of individual mass and position. So each particle with its own unique mass is some unique distance away from a reference point. If we continually add all these particles together we will get the entire mass of the object and the total length. The distribution of these different masses at different positions will affect the location of the center of mass, the average position of all the particles of mass that make up an object.
The center of gravity (CG) is the same point if the object is in a uniform gravitational field
Let's consider the figure , a system of two particles, mA and mB,
that are located at positions xA and xB away from the origin.
a) If mA > mB, predict where xCM is located.
b) If mA < mB, predict where xCM is located.
c) If mA = mB, predict where xCM is located.
To calculate xCM, use the following equation.
xCM = mA xA + mB xB / (mA + mB)
Practice: Solve if xA = 10 cm, mA = 4 kg, xB = 40 cm, mB = 2 kg
The more particles in a system, the more terms added to the top and bottom of the previous equation. The general form follows:
xCM = Σ(m x) / Σm
If there is more than one dimension, then the location of the center of mass for each direction (X, Y & Z) should be calculated and the location described using each.
The center of mass can be found experimentally by balancing the object at one point.
Center of Mass.notebook December 16, 2015
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