Example&Acirc;&nbsp;9-16

# Example&Acirc;&nbsp;9-16 - Mgh Because the sphere...

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Example 9-16 A Bowling Ball A bowling ball that has an 11-cm radius and a 7.2-kg mass is rolling without slipping at 2.0 m/s on  a horizontal ball return. It continues to roll without slipping up a hill to a height  h  before  momentarily coming to rest and then rolling back down the hill. Model the bowling ball as a  uniform sphere and find  h . PICTURE  No slipping occurs, so no energy is dissipated by kinetic friction. No external forces act  on the ball–hill–Earth system, so no external forces do work on the system. The initial kinetic  energy, which is the translational kinetic energy, , plus the kinetic energy of rotation about the  center of mass, , is converted to potential energy

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Unformatted text preview: Mgh . Because the sphere rolls without slipping, the initial linear and angular speeds are related by SOLVE 1. Make a labeled sketch showing the ball in both its initial and final positions ( Figure 9-34 ). 2. No external forces act on the system, so the work done by external forces is zero, and no slipping occurs, so no energy is dissipated by kinetic friction. Thus, mechanical energy is constant: Answer: 3. Apply conservation of mechanical energy with U i = 0 and K f = 0. Write the total initial kinetic energy K i in terms of the speed and the angular speed ω 1 : Answer: 4. Substitute from and solve for h : Answer:...
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