Solving a Ball Roll Down a Slide: Velocity at Bottom

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SUMMARY

The discussion focuses on calculating the velocity of a ball, modeled as a thin spherical shell, at the bottom of a slide with a height of 4 meters. The relevant equation for this problem is the conservation of mechanical energy, expressed as KE(i) + PE(i) + Iw(i) = KE(f) + PE(f) + Iw(f). The moment of inertia for the ball is given by Icm=(2/3)mr^2, which is crucial for determining the final velocity. The correct approach involves recognizing that Iw represents angular momentum, not energy, and applying the conservation principles accurately.

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  • Understanding of conservation of mechanical energy principles
  • Familiarity with kinetic and potential energy equations
  • Knowledge of moment of inertia for thin spherical shells
  • Basic concepts of angular momentum
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Homework Statement



A toddler is having fun rolling a ball down a slide of height h=4 m. The ball can be considered as a thin spherical shell, Icm=(2/3)mr^2, with m being its mass and r being its radius. What is the velocity of the ball at the bottom of the slide?

http://schubert.tmcc.edu/enc/51/76a002f3ae50dbbab12d33cf0762512f807c557c31b679999d542c0ad5867fc1faec19c5cc0644a0057420a72734c009d46cf669ed738b61fc0def4a303f9990.gif

Homework Equations



KE(i) + PE(i) + Iw(i) = KE(f) + PE (f) + Iw(f)

KE(i) = Initial Kinetic Energy
PE(i) = Initial Potential Energy
Iw(i) = Initial Inertia*Omega

KE(f) = Final Kinetic Energy
PE(f) = Final Potential Energy
Iw(f) = Final Inertia*Omega

The Attempt at a Solution



I think I am supposed to use the above equation but I am not quite sure. Any suggestions? Thanks.
 
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You want to use conservation of mechanical energy, don't you? But Iw is not energy. It is angular momentum.

ehild
 
So, what do I do with this value: Icm=(2/3)mr^2? I am sure that it plays a part in solving for the solution.
 

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