Download Calculations

These are the calculations for determining different velocities:
Given: Bocce ball mass and diameter, pallina mass and diameter, coefficients of friction (rolling, kinetic
And static)
Find: a. Minimum velocity needed to travel 60 feet, b. velocity required to break up a cluster of bocce
Balls at 59 feet (distance bocce will travel after collision is 1 foot) and c. if the bocce ball will
Be slipping or rolling down the ramp
Assumptions: 1. No slip (v=r )
2. Constant deceleration
3. All velocities are located at C of G for simplicity
4. Conservation of energy
5. Ball does not “bounce” or “hop”
6. Perfectly elastic collisions
Governing Equations:
:
:
FBD:
Formulas Used for Calculations
Final velocity required to go 18.3 m:
Height required to gain enough velocity to go 18.3 m:
Feasibility analysis to determine if slipping down the ramp occurs:
The ball will roll without slipping if the tangential force, ft , is less than the force due to static friction, fs.
:
:
Solving for the tangential force shows that some slipping does occur. The only way to mitigate this
sliding motion is by utilizing a ramp profile with a maximum angle of 30°. Unfortunately this shallow an
angle would not allow for sufficient momentum for the ball to go the required 18.3 m.