Accelerating a Uniform Sphere Down an Incline

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Homework Help Overview

The problem involves a uniform sphere rolling down a 30-degree incline from a height, with the goal of finding the acceleration of its center of mass. The original poster expresses uncertainty about how to start the problem, particularly in relating energy concepts to acceleration.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to use energy formulas but is unsure how to derive acceleration from them. Some participants suggest correcting the approach and finding the length traveled to apply kinematic relations.

Discussion Status

Participants are engaging in clarifying the setup and exploring different aspects of the problem. Guidance has been offered regarding the potential energy and the relationship between distance traveled and acceleration, although the original poster's understanding appears to be evolving.

Contextual Notes

The original poster indicates a need for guidance on formulas and setup, suggesting possible constraints in their understanding of the relationship between energy and motion in this context.

physikx
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Homework Statement


A uniform sphere rolls down a 30 degree incline θ from height h. Initially, the solid is at rest. Find the acceleration for the center of the mass of the solid.

I am not sure where to start with this problem. I started with the energy formulas, but I am not sure how to find the acceleration of the center of mass from there. I just need a guide on what formulas or setup to use, thanks!

Homework Equations


Translational and rotational motion equations

The Attempt at a Solution


K_i=mghsin30
K_f=1/2mv^2+1/2Iω^2

then I solved for v:
v=radical(10/7*ghsin30)
 
Last edited:
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Hi, physikx,

The potential energy is mgh (h is the height of the (slope). Correct your result for v.

V is the speed of the CM at the end of the slope. Find the length travelled, and use the relation s=v^2/(2a) to determine the acceleration of the CM.

ehild
 
Hey ehid,

Thank you so much for the help! I was able to setup the problem and get the answer. I really appreciate the guidance.

Peace
 
You are welcome.

ehild
 

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