<< Chapter < Page Chapter >> Page >

Validation

We can compute the total mechanical energy at this point as

PEg = m*g*h = 10kg * (9.8m/s^2) * 413m = 40474 joules

This result is close enough to the total mechanical energy at the end of Leg B to validate the computations. In this case, we determined the height usingtime, velocity, and acceleration, and validated that height using work/energy concepts.

State at the end of Leg C

At the completion of Leg C:

  • The rocket is at the apex at a height of 413 meters.
  • The total mechanical energy is 40470 joules.
  • The kinetic energy is 0 because for an instant, the rocket isn't moving.
  • The mechanical energy consists totally of gravitational potential energy.

Leg D

Leg D of the trip is fairly simple. The rocket falls for a distance of 413 meters under the influence of the internal gravitational force.

No change in mechanical energy

Once again, because the force is an internal force, the total mechanical energy cannot be changed by the work done by the force. However, the mechanicalenergy can be transformed from potential energy to kinetic energy.

At the instant before the rocket strikes the ground, it must still have a total mechanical energy value of 40470 joules.

Kinetic energy: 40470, potential energy: 0

At the instant before the rocket strikes the ground, all of the mechanical energy has been transformed into kinetic energy. We can use that knowledge tocompute the velocity of the rocket right before it strikes the ground.

KE = 0.5*m*v^2, or

v^2 = KE/(0.5*m), or

v = (KE/(0.5*m))^(1/2) = (40470 joules/(0.5*10kg))^(1/2), or

terminal velocity = v = 90 meters/sec

Thus, the terminal velocity of the rocket when it strikes the ground is 90 meters/sec straight down.

Validation

Let's see if we can validate that result using a different approach. Given the height of the apex and theacceleration of gravity, we can computer the transit time as

413m = 0.5*g*t^2, or

t^2 = 413m/(0.5*g), or

t = (413m/(0.5*g))^(1/2) = (413m/(0.5*9.8m/s^2))^(1/2), or

t = 9.18 seconds

Compute the terminal velocity

Knowing the time to make the trip to the ground along with the acceleration, we can compute the terminal velocity as

v = g * t = (9.8m/s^2)*9.18s = 90 m/s

which matches the terminal velocity arrived at on the basis of work and energy.

State at the end of Leg D

Therefore, at the end of Leg D, the rocket crashes into the ground. However, an instant before the crash,

  • The total mechanical energy is 40470 joules.
  • The gravitational potential energy is 0.
  • The kinetic energy is 40470 joules.
  • The velocity is 90 m/s straight down toward the center of the earth.

Do the calculations

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.

Resources

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.

Miscellaneous

This section contains a variety of miscellaneous information.

Housekeeping material
  • Module name: Relationships Among Kinematics, Newton's Laws, Vectors, 2D Motion, 2D Forces, Momentum, Work, Energy, and Power
  • File: Phy1220.htm
  • Revised: 10/02/15
  • Keywords:
    • physics
    • accessible
    • accessibility
    • blind
    • graph board
    • protractor
    • screen reader
    • refreshable Braille display
    • JavaScript
    • trigonometry
    • potential energy
    • work
    • gravitational potential energy
    • elastic potential energy
    • kinetic energy
    • mechanical energy
    • total mechanical energy
    • power
    • watt
    • internal force
    • conservative force
    • external force
    • non-conservative force
Disclaimers:

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-

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Accessible physics concepts for blind students. OpenStax CNX. Oct 02, 2015 Download for free at https://legacy.cnx.org/content/col11294/1.36
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Accessible physics concepts for blind students' conversation and receive update notifications?

Ask