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 [:RigidBodies#FindingCofG: 1J10. Statistics of Rigid Bodies, Finding the Center of Gravity]  [[RigidBodies#FindingCofG| 1J10. Statistics of Rigid Bodies, Finding the Center of Gravity]]
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 * '''Cabinet:''' [:MechanicsCabinet:Mechanic (ME)]
 * '''Bay:''' [:MechanicsCabinetBayA6:(A6)]
 * '''Cabinet:''' [[MechanicsCabinet|Mechanic (ME)]]
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 * [https://www.youtube.com/user/LectureDemostrations/videos?view=1 Lecture Demonstration's Youtube Channel]  * [[https://www.youtube.com/user/LectureDemostrations/videos?view=1|Lecture Demonstration's Youtube Channel]]
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 * [https://en.wikipedia.org/wiki/Center_of_mass Center of Gravity (Center of Mass) - Wikipedia]  * [[https://en.wikipedia.org/wiki/Center_of_mass|Center of Gravity (Center of Mass) - Wikipedia]]
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[:Instructional:Home] [[Instructional|Home]]

Table of Mechanics Demonstration

List of Mechanics Equipment & Supplies

Lecture Demonstrations

Wooden State Maps, 1J10.11

Topic and Concept:

Location:

WoodenState02-400.jpg

Abstract:

Suspend a map of the state from holes drilled at various points to find the "center of the state".

Equipment

Location

ID Number

Wooden State Map

ME, Bay A6, Shelf #4

Plumb Bob

ME, Bay A6, Shelf #4

Rod Stand

Rod and Clamp Cabinet

Important Setup Notes:

  • N/A

Setup and Procedure:

  1. Instead of a weighted rod stand as pictured, a rod clamped to the lecture bench works well too.
  2. Make sure there are two smaller rods cantilevered off the vertical rod.
  3. From each eyebolt, suspend the wooden state, and hang the plumb bob from the higher rod.
  4. For each suspension point, trace a line along the string of the plumb bob using a dry-erase marker.
  5. Draw a point on the location where all of these lines intersect. This is the center of gravity.

Cautions, Warnings, or Safety Concerns:

  • N/A

Discussion:

The orientation of the state map while suspended from the rod is determined by the collective effect of gravity on each mass element of the map. For each point of mass in the board not in the center of mass, there will be a torque on the board due to gravity. The equilibrium orientation of the state map is the configuration of zero torque. The center of mass will always be located under the suspension point (on the line traced by the plumb bob). The point where all these lines intersect is the point where the sum of the position vectors for every mass element, weighted by mass, is zero. I.e. where Σi ri * mi = 0.

PlumbBob01-250.jpg

WoodenState03-250.jpg

WoodenState05-250.jpg

WoodenState06-250.jpg

WoodenState07-250.jpg

WoodenState08-250.jpg

WoodenState09-250.jpg

WoodenState10-250.jpg

Videos:

References:

Home

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