0.15 Phy1120: force -- center of gravity  (Page 4/8)

A void in a 3D object

It is also possible for the C.G. to be located in a cavity in a three-dimensional object. For example, the C.G. for a small sectionof cylindrical pipe that is cut square on both ends would be in the center of the void half way between the ends of the pipe.

Discussion and computations

Creation of tactile graphics

The module titled Manual Creation of Tactile Graphics explains how to create tactile graphics from svg files that I will provide.

If you are going to have an assistant create tactile graphics for this module, you will need to download the file named Phy1120.zip , which contains the svg files for this module. Extract the svg files from the zip file and provide them to your assistant.

Also, if you are going to use tactile graphics, it probably won't be necessary for you to perform the graph board exercises. However, you shouldstill walk through the graph board exercises in your mind because I will often embed important physics concepts in the instructions for doing the graph boardexercises.

In each case where I am providing an svg file for the creation of tactile graphics, I will identify the name of the appropriate svg file and display animage of the contents of the file for the benefit of your assistant. As explained here , those images will will be mirror images of the actual images so that your assistant can emboss the image from the back ofthe paper and you can explore it from the front.

I will also display a non-mirror-image version of the image so that your assistant can easily read the text in the image.

Also in those cases, I will provide a table of key-value pairs that explain how the Braille keys in the image relate to text or objects in the image.

Equilibrium: stable, unstable, and neutral

When a vertical line through the C.G. of a body falls within the area covered by the supportingbase, the body can rest in equilibrium. A body in equilibrium can be further qualified as being either stable, unstable, or neutral.

• Stable equilibrium: If a body at rest receives a small displacement and tends to return to its former position, that body is said to be in stable equilibrium.
• Unstable equilibrium: If that body tends to move further away, then that body is said to be in unstableequilibrium.
• Neutral equilibrium: If it does neither, the body is said to be in neutral equilibrium.

A practical example

Consider the case of a round pencil, sharpened on one end and flat on the other end. If you lay the pencil flat on the table and give it a very smallpush, it will move and then stop. That pencil is said to be in neutral equilibrium. It doesn't tend to return to its original position, and except forrolling a small distance as a result of inertia, it doesn't tend to move further away.

Balance it on the flat end

If you balance the pencil on its flat end and give it a very small push at the other end, it will tip slightly and then return to its original position.This assumes that you don't push it beyond its tipping point, which we will discuss in more detail later.