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In order to understand the full importance of these laws, it is necessary to understand the concepts of and relationships among mass, momentum, force, andacceleration.
Newton introduced the term mass as being distinct from weight . Mass is not easy to define in its own right. Mass can be thought of as being a "quantity ofmatter" or a "measure of inertia."
One of the properties of mass in a gravitational field is weight. Newton showed that weight is proportional to mass.
(In earlier modules, we have said that the weight of a body is a measure of the force required to cause that body to accelerate toward the surface of theearth at a rate of approximately 32.2 ft/s^2 or 9.81 m/s^2.)
Newton also worked with the concept of momentum , which is the product of the mass and the velocity of an object. Momentum is a vectorquantity, having the same direction as the velocity to which it applies. Therefore, momenta are always added or subtracted as vectors.
The rate of change of momentum
As indicated in the second law , the force required to bring about a change in momentum is proportional to the rate of change of themomentum:
F $ (m*v2 - m*v1)/t
where the momentum is changed from a value of m*v1 to a value of m*v2 in a time interval t .
(Note that I elected to use the $ character to indicate "is proportional to." Textbooks typically use a Greek letter for this purpose, which is not compatiblewith many Braille displays and some audio screen readers.)
Given that the mass is constant (for the scenarios addressed in this collection of modules), and acceleration is given by the rate of change ofvelocity, factoring mass out of the above equation gives us
F $ m*(v2 - v1)/t, or
F $ m*a
where a is acceleration. Thus, force is proportional to the product of mass and acceleration. For a given mass, a specific force is required to cause thatmass to accelerate by a given amount.
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.
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