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The box on the left would need to rotate slightly more than 45 degrees clockwise around point b before the direction of the weight vector through the C.G. would moveto the right of point b, causing the box to continue rotating under its own weight.
However, the box on the right would only need to rotate slightly more than 14 degrees clockwise around point b before the direction of the weight vector through the C.G. would move to the right of point b causing the box to continue rotating under itsown weight.
Conclusion
Therefore, the box on the left is more stable than the box on the right. If you want to lessen the likelihood of an object tipping over, cause the C.G. of the object to be near the bottomof the object.
An exercise for the student
I will leave it as an exercise for the student to compute moments about point b to confirm the tipping angle for each box where the torque about point bchanges from counter-clockwise to clockwise.
Let me illustrate this situation with a real-world example that may seem familiar to you. Assume that you put some flowers with long stems in alightweight plastic vase and set the vase on a table. The C.G. of the vase and the flowers would be relatively high, and it wouldn't take much of a sidewayspush to cause the vase to turn over.
Now assume that you add water to the vase until it is about half full. This would cause the C.G. of the vase, the water, and the flowers to move down,probably into the bottom half of the vase. This would make it more difficult to tip the vase over. Of course, when it does tip over, it would make a bigger mess than would be the case without the water.
I encourage you to repeat the computations that I have performed in this module. Experiment withthe computations, making changes, and observing the results of your changes. Make certain that you can explain why your changes behave as they do.
I will publish a module containing consolidated links to resources on my Connexions web page and will update and add to the list as additional modulesin this collection are published.
This section contains a variety of miscellaneous information.
Financial : Although the openstax CNX site makes it possible for you to download a PDF file for the collection that contains thismodule at no charge, and also makes it possible for you to purchase a pre-printed version of the PDF file, you should beaware that some of the HTML elements in this module may not translate well into PDF.
You also need to know that Prof. Baldwin receives no financial compensation from openstax CNX even if you purchase the PDF version of the collection.
In the past, unknown individuals have copied Prof. Baldwin's modules from cnx.org, converted them to Kindle books, and placed them for sale on Amazon.com showing Prof. Baldwin as the author.Prof. Baldwin neither receives compensation for those sales nor does he know who doesreceive compensation. If you purchase such a book, please be aware that it is a copy of a collection that is freelyavailable on openstax CNX and that it was made and published without the prior knowledge of Prof. Baldwin.
Affiliation : Prof. Baldwin is a professor of Computer Information Technology at Austin Community College in Austin, TX.
-end-
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