View Single Post
  #4   Spotlight this post!  
Unread 17-02-2006, 10:16
JoeXIII'007's Avatar
JoeXIII'007 JoeXIII'007 is offline
Pragmatic Strategy, I try...
AKA: Joeseph Smith
FRC #0066
Team Role: Alumni
 
Join Date: Feb 2004
Rookie Year: 2001
Location: Ypsilanti, MI (Ann Arbor's shadow)
Posts: 753
JoeXIII'007 has a reputation beyond reputeJoeXIII'007 has a reputation beyond reputeJoeXIII'007 has a reputation beyond reputeJoeXIII'007 has a reputation beyond reputeJoeXIII'007 has a reputation beyond reputeJoeXIII'007 has a reputation beyond reputeJoeXIII'007 has a reputation beyond reputeJoeXIII'007 has a reputation beyond reputeJoeXIII'007 has a reputation beyond reputeJoeXIII'007 has a reputation beyond reputeJoeXIII'007 has a reputation beyond repute
Send a message via AIM to JoeXIII'007
Re: Physics: ball launch using gravity

Quote:
Originally Posted by Tom Bottiglieri
As David said...

Total energy is a system is constant.
Code:
Potential Energy (U)  = (mass) * (height) * (acceleration of gravity)
Linear Kinetic Energy (T) = 1/2 * (mass) * (velocity ^ 2)
Rotational Kinetic Energy (KR) = 1/2 * (moment of inertia) * (velocity ^ 2)

I for a sphere: 2/5 * Mass * Radius^2

EA = EB (E is total energy, A and B are arbitrary points in time.)

E = T + U + KR
So what I would do first is a simple kinematics/projectile motion problem (there might be some handy tools in the white paper section ) to find what velocity is needed on the launch. (In this case, you would arbitrarily chose the angle theta of the launch. I would chose 45 degrees.)

Once you have your needed velocity and launch angle, figure out how much kinetic energy it will have at launch. Plug the velocity, mass, and Moment of Inertia (I) into the equations above, and add the 2 values together to find net kinetic energy. Then, set that equal to the potential energy (You can assume this if your reference frame has the balls launch point as (0,0) and the ball is starting from a stop, aka no kinetic energy.)

So now you have U = T + KR and U = mgh. Simply solve for U, and divide by 0.098 (g * m) to find how high (in meters) your ball should start in the y direction above the launch point.

Voila.
Thank you. This should work really well.

-Joe
__________________
Joeseph P. Smith
jpthesmithe.com
University of Michigan - Informatics (B. Sci. 2012)
General Purpose Programmer - Cooperative Institute for Limnology and Ecosystems Research (CILER) at NOAA-GLERL
Reply With Quote