What is its linear speed at the bottom of the incline?

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Homework Help Overview

The problem involves a spherical object rolling down an incline, focusing on determining its linear speed at the bottom. The context includes concepts of energy conservation and rotational dynamics, specifically relating to moment of inertia.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of energy conservation principles, attempting to relate potential energy to kinetic energy for both translational and rotational motion. There are questions about the correct formulation of equations and the placement of parentheses in mathematical expressions.

Discussion Status

The discussion is active, with participants offering feedback on the mathematical approach used. There is acknowledgment of a correct method, but also a focus on clarifying notation and ensuring proper expression of the equations involved.

Contextual Notes

Participants are navigating the complexities of rolling motion and the implications of moment of inertia in their calculations. There is an emphasis on ensuring clarity in mathematical representation, which may affect understanding of the solution process.

jimmyboykun
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Homework Statement


A spherical object with a moment of inertia of 0.584mr2 starts from rest rolling down a 2.25-m high incline. If the sphere is rolling without slipping


Homework Equations


I the best equation to use for this problem is k(initial)+u(initial)=k(final)+u(final)


The Attempt at a Solution


I stretch the equation 1/2mv^2(initial)+1/2Iω^(initial)+mgh(initial)=1/2mv^2(final)+1/2Iω^2(final)+mgh(final).

since the object started from rest the initial kinetic energy and the final potential energy is zero, which leads me to this equation

mgh(initial)=1/2mv^2(final)+1/20.584mr^2ω^2(final). As I continue reduce the equations I round up with this.

gh(initial)=0.792v^2(final)

v=sqrt(9.81m/s^2)(2.25m)/0.792

the linear speed I came up with was 5.279m/s.

Did I do this right?
 
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jimmyboykun said:
v=sqrt(9.81m/s^2)(2.25m)/0.792
The parentheses aren't written correctly there, but the method's fine and I agree with your final answer.
 
haruspex said:
The parentheses aren't written correctly there, but the method's fine and I agree with your final answer.

How would I write the parentheses the correct way?
 
jimmyboykun said:
How would I write the parentheses the correct way?

sqrt((9.81m/s^2)(2.25m)/0.792)
 

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