Differences between revisions 8 and 9
 ⇤ ← Revision 8 as of 2013-07-12 18:17:55 → Size: 2825 Editor: localhost Comment: converted to 1.6 markup ← Revision 9 as of 2016-06-23 21:13:59 → ⇥ Size: 2990 Editor: srnarf Comment: Deletions are marked like this. Additions are marked like this. Line 2: Line 2: ||<:30%>[[PiraScheme#Mechanics| Table of Mechanics Demonstration]]||<:30%>[[MEEquipmentList| List of Mechanics Equipment & Supplies]]||<:30%>[[Demonstrations|Lecture Demonstrations]]|| ||<30%  style="text-align:center">[[PiraScheme#Mechanics|Table of Mechanics Demonstration]] ||<30%  style="text-align:center">[[MEEquipmentList|List of Mechanics Equipment & Supplies]] ||<30%  style="text-align:center">[[Demonstrations|Lecture Demonstrations]] || Line 5: Line 6: '''Topic and Concept:''' Line 6: Line 8: '''Topic and Concept:''' [[RigidBodies#FindingCofG| 1J10. Statistics of Rigid Bodies, Finding the Center of Gravity]] . [[RigidBodies#FindingCofG|1J10. Statics of Rigid Bodies, Finding the Center of Gravity]] Line 10: Line 11: Line 12: Line 14: * '''Shelf:''' #4 * '''Shelf:''' #4 Line 19: Line 21: ||<:style="width: 60%" :40%>'''Equipment'''||<:30%>'''Location'''||<:25%>'''ID Number'''|| ||<40% style="text-align:center">'''Equipment''' ||<30%  style="text-align:center">'''Location''' ||<25%  style="text-align:center">'''ID Number''' || Line 22: Line 23: ||Wooden State Map||ME, Bay A6, Shelf #4|| ||||Plumb Bob||ME, Bay A6, Shelf #4|| ||||Rod Stand||Rod and Clamp Cabinet|| || ||Wooden State Map ||ME, Bay A6, Shelf #4 || ||||Plumb Bob ||ME, Bay A6, Shelf #4 || ||||Rod Stand ||Rod and Clamp Cabinet || || Line 27: Line 28: '''''Important Setup Notes:'''''  * N/A Line 31: Line 30: '''Setup and Procedure:''' '''''Important Setup Notes:''''' * N/A'''Setup and Procedure:''' Line 40: Line 43: Line 42: Line 46: '''Discussion:''' '''Discussion:''' Line 46: Line 49: || {{attachment:PlumbBob01-250.jpg}} || {{attachment:WoodenState03-250.jpg}} || {{attachment:WoodenState05-250.jpg}} || {{attachment:WoodenState06-250.jpg}} |||| {{attachment:WoodenState07-250.jpg}} || {{attachment:WoodenState08-250.jpg}} || {{attachment:WoodenState09-250.jpg}} || {{attachment:WoodenState10-250.jpg}} || Line 47: Line 52: ||{{attachment:PlumbBob01-250.jpg}}||{{attachment:WoodenState03-250.jpg}}||{{attachment:WoodenState05-250.jpg}}||{{attachment:WoodenState06-250.jpg}}||||{{attachment:WoodenState07-250.jpg}}||{{attachment:WoodenState08-250.jpg}}||{{attachment:WoodenState09-250.jpg}}||{{attachment:WoodenState10-250.jpg}}|| Line 51: Line 56: Line 57: Line 63:

# Wooden State Maps, 1J10.11

Topic and Concept:

Location:

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.

Videos:

References:

fw: Wooden_State_Map (last edited 2016-06-23 21:13:59 by srnarf)