×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Jobs

Kinetics of a released elastic band

Kinetics of a released elastic band

Kinetics of a released elastic band

(OP)
My problem is to calculate the final velocity of a small mass, m, tied to the end of an elastic band that is pulled and released. I know how to do this in the simple case:  potential energy of the elastic (spring)equals kinetic energy of the mass.  The challenge is that the mass of the elastic band may be significant in that it too will have significant kinetic energy so that the final velocity of the small mass will be less if the band soaks up kinetic also. [The elastic of course stretches and the elemental kinetic energy varies along its length]. Any ideas?

RE: Kinetics of a released elastic band

The effective mass of the rubber band is 1/3 of its total mass.  This is assuming 1 end fixed, the other end moving.  

If a mode shape is defined by a function Phi, then the effective mass is equal to the integral of (mass per unit length) times Phi^2, integrated over the length.  In your case, Phi(x) = x, m = mass/length, and effective mass is m*L/3.

RE: Kinetics of a released elastic band

OOPS, I hit post a little too quickly.  My previous post gives the effective mass of the elastic band only.  The mass of your object must be added to this to get the total effective mass.  If you use the combined effective mass, then you can use conservation of energy to solve for the particle velocity.

RE: Kinetics of a released elastic band

The force in the band could be found by:

F=100(DeltaL/OrigL)/(Elonation%*TensleStress*Area)

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Resources