The Inclined Plane Race: Sphere vs. Hoop

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Homework Help Overview

The discussion revolves around a problem involving a sphere and a hoop of equal mass rolling down an inclined plane without slipping. Participants are exploring the dynamics of rolling motion, specifically comparing the time it takes for each object to reach the bottom and their kinetic energies at that point.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the effects of different moments of inertia on the motion of the sphere and hoop. There is also a consideration of the relationship between potential energy and kinetic energy in the context of rolling objects.

Discussion Status

Some participants have provided insights into the differences in kinetic and rotational energy for the two objects, suggesting that the hoop will be slower due to its moment of inertia. However, there is no explicit consensus on the final outcomes or the implications of these differences.

Contextual Notes

One participant clarifies that the problem is sourced from a book rather than being a homework assignment, indicating a desire to understand the concepts involved rather than seeking direct solutions.

Tricks67
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a sphere and a hoop both of same mass (e.g. 'm') roll down an inclined plane without slipping...which will get to the bottom first..will they have equal kinetic energies when they reach the bottom?
 
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This appears to be homework. If so, you're supposed to show some attempt at solving the problem.
 
nope not hw..(i wish our homework wud have had such long deadlines)...some problems given in a book...and i post the ones, i can't approach..
 
Tricks67 said:
nope not hw..(i wish our homework wud have had such long deadlines)...some problems given in a book...and i post the ones, i can't approach..

No... though both objects have the same potential Energy at t = 0s, they have different "moments of inertia" and since they are both rolling they have both kinetic and rotational Energy when they reach the bottom of the inclined plane. The hoop will be slower.

Erot = 1/2 J ω²
 

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