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More on the crate and the ramp
How much work was done on the crate in pushing it to the top of the ramp?
Answer:
The first task is to compute the force parallel to the ramp that is required to push the crate up the ramp, ignoring the extra push required to get it movingat the bottom of the ramp. That parallel force is equal to the component of the crate's weight that is pushing down parallel to the ramp.
A little trigonometry will reveal that the component of the crate's weight that is parallel to the ramp isequal to the product of the total weight of the crate and the sine of the ramp angle relative to the horizontal ground. That gives us a requirement for a forcepushing up the ramp and parallel to the ramp of
(100 kg) * 9.8 (m / (s^2)) * sin(36.9 degrees) = 588 newtons
The angle between the line of action of the force and the displacement direction of the crate was 0 degrees. Therefore, the work done on the crate was:
(588 newtons) * 5 m * cos(0) = 2940 joules
Note that the work done on the crate to move it to its new position was equal to the change in gravitational potential energy for the crate. As you may haveguessed, that is not a coincidence. You will learn more about that relationship in a future module.
I encourage you to repeat the calculations that I have presented in this lesson to confirm that you get the same results. Experiment with the scenarios, 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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