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Center of Mass

Center of Mass. 7.5. Center of Mass. Mass can be located in several places in a problem Two skaters, a hockey puck and a mitten, etc. Center of Mass (cm) = “average” location of all the mass It’s as if all the mass were in one spot. Center of Mass – 1-D. 2 point masses on x-axis

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Center of Mass

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  1. Center of Mass 7.5

  2. Center of Mass • Mass can be located in several places in a problem • Two skaters, a hockey puck and a mitten, etc. • Center of Mass (cm) = “average” location of all the mass • It’s as if all the mass were in one spot

  3. Center of Mass – 1-D • 2 point masses on x-axis • cm should be closer to more massive point

  4. Center of Mass – 1-D • For more than 2 points • For macroscopic objects • Evenly distributed mass  cm is in center • Spheres, cubes, rectangular prisms, etc. • Unevenly distributed mass  cm is nearer the most massive portion • Golf clubs, people, chairs, etc.

  5. Center of Mass – 2-D • For more than 1-D • Same equations for cm, but done once for each dimension

  6. Example - cm • Two marbles, shooter (m = .01 kg) and a regular marble (m = .005 kg) are .2 m apart where is the center of mass in relation to the shooter? • xcm = .0667 m from the shooter towards the other marble

  7. Velocity of CM • The numerator is the total momentum • Since momentum doesn’t change, the vcm doesn’t change • The center of mass will travel in a straight line at a constant speed

  8. Example • Two marbles, shooter (m = .01 kg) moving at 0.5 m/s hits a regular marble (m = .005 kg) at rest. If it is an elastic collision, find the final velocities of the marbles. • vr = .67 m/s, vs = .17 m/s • Find the velocity of the center of mass before and after the collision. • vcm = .33 m/s

  9. Practice Work • Change the center of mass of your paper and pencil (by transferring the lead) while doing these problems • 200 CQ18-20, P41-43 • Total of 6 problems

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