0.15 Phy1120: force -- center of gravity  (Page 3/8)

When the string is attached to an object that is fixed relative to the surface of the earth and the plummet is allowed to hang down, it will eventually (whenit stops swinging) point directly at the center of mass of the earth.

Common uses for a plummet

The plummet is most commonly used in construction projects to ensure that constructions are "plumb", or vertical.

It is also used in land surveying to set a surveying instrument exactly over a fixed survey marker, or to transcribe positions onto the ground for placing amarker.

Experimental verification of the C.G.

I'm aware that as a blind student, you probably can't perform this experiment, but hopefully you can imagine it.

Make a hanger

Use a plummet to draw a vertical line on a flat, smooth, vertical surface (such as a wall). Drive a finishing nail (a nail with a small head) into thesurface on the vertical line allowing a small portion of the nail to stick out. Cause the nail to be as horizontal as practical.

Make an irregular object

Cut an irregular shape out of a piece of flat cardboard and punch several holes around the perimeter of the shape.

Perform the experiment

Using several holes in succession, including holes on all four sides of the cardboard, hang the cardboard on the nail in such a way that the cardboard isfree to swing and settle into a stable orientation.

Once the cardboard stops swinging, mark the point on the bottom of the cardboard that coincides with the vertical line that you drew on the verticalsurface.

After you have done this several times, draw lines from each hole to the corresponding markthat you made on the opposite edge of the cardboard. All of these lines should cross at a single point. That point is the C.G. for that particularirregular shape of cardboard.

Modify the experiment

Cut regular shapes of cardboard such as rectangles, triangles, hexagons, octagons, etc, and repeat the experiment with those shapes. Observe the locationof the C.G. for those shapes.

Rectangular shapes

You should find that the C.G. for a rectangular piece of cardboard is at the center of the rectangle. This should be the case for allrectangles ranging from squares to long skinny rectangles (although it may difficult to measure for long skinny rectangles.)

Triangular shapes

The C.G. for a triangular shape should be at the intersection of its medians.

In case you have forgotten, the median of a triangle is a line segment from a vertex of the triangle to the midpoint of the side opposite that vertex. Because there are three vertices, there are three medians. No matter what shape the triangle, all three medians intersect at a single point,which is called the centroid of the triangle. That point would also be the C.G. for a triangular-shaped piece of cardboard.

The doughnut hole

Cut a piece of cardboard in the general shape of a doughnut or tire with a hole in the middle andperform the experiment using that shape. Observe that the C.G. can be located in the doughnut hole. The C.G. of an object doesn't have to be in asolid part of the object.