View Single Post
  #3   Spotlight this post!  
Unread 17-02-2006, 00:59
Tom Bottiglieri Tom Bottiglieri is offline
Registered User
FRC #0254 (The Cheesy Poofs)
Team Role: Engineer
 
Join Date: Jan 2004
Rookie Year: 2003
Location: San Francisco, CA
Posts: 3,185
Tom Bottiglieri has a reputation beyond reputeTom Bottiglieri has a reputation beyond reputeTom Bottiglieri has a reputation beyond reputeTom Bottiglieri has a reputation beyond reputeTom Bottiglieri has a reputation beyond reputeTom Bottiglieri has a reputation beyond reputeTom Bottiglieri has a reputation beyond reputeTom Bottiglieri has a reputation beyond reputeTom Bottiglieri has a reputation beyond reputeTom Bottiglieri has a reputation beyond reputeTom Bottiglieri has a reputation beyond repute
Re: Physics: ball launch using gravity

Quote:
Originally Posted by David Brinza
Using conservation of energy, you should be able to determine from what height you will need to start rolling the ball down a "ski jump" in order to achieve enough velocity to launch the ball at some angle to make it through the hoop. Don't forget to include the rotational energy of the ball in your calculation...
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.
Reply With Quote