Sphere on Incline: Kinetic Energy of a Rolling Sphere

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Homework Help Overview

The discussion revolves around a solid sphere rolling down an incline without slipping, specifically focusing on the translational kinetic energy at the bottom of the incline under different conditions, including a frictionless scenario.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the implications of friction on the sphere's motion, questioning how kinetic energy is affected in both rolling and slipping scenarios. There is an exploration of the relationship between potential energy and kinetic energy in the context of the problem.

Discussion Status

Some participants have made progress in calculating velocity and are considering the effects of different conditions on kinetic energy. There is an acknowledgment of incomplete information in the problem statement, and participants are exploring various interpretations of the energy transformations involved.

Contextual Notes

Participants note the absence of friction in one scenario and question how this affects the energy distribution between translational and rotational forms. There is also mention of the need to consider the moment of inertia when discussing rolling motion.

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A solid sphere of uniform density starts from rest and rolls without slipping a distance of d = 3.9 m down a q = 35° incline. The sphere has a mass M = 4.6 kg and a radius R = 0.28 m.
https://online-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys101/fall07/homework/08/03/3.gif

Suppose now that there is no frictional force between the sphere and the incline. Now, what is the translational kinetic energy of the sphere at the bottom of the incline?
 
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I figured out that the velocity is 5.6 m/s, but I don't know what the KE tran would be at the bottom without friction.
 
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The problem statement is incomplete, but I infer that you are being asked for the translational KE at the bottom for the two cases: the ball rolls down the incline, or it just slips down the incline (frictionless case).

If it just slips, then the KE final equals the PE initial, right? Why?

If it rolls, then some energy goes into the rolling motion (look up moment of inertia). What is the equation for the rotational energy of a sphere? What does that do to the final KE of the sphere at the bottom?
 
nvm i figured it out.
 
Doh!
 

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