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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.