Solving Solid Disk Rolling Up Incline: Find Height h

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Homework Help Overview

The problem involves a solid disk of mass m and radius R rolling up an incline without slipping, and the goal is to determine how far vertically it will rise given its initial velocity v. The discussion centers around the conversion of kinetic energy to potential energy in this context.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between kinetic and potential energy, considering the equations for rotational and translational motion. There is an exploration of how to express height h in terms of the disk's initial velocity and its angular velocity ω. One participant questions the presence of ω in their derived expression for h.

Discussion Status

Some participants have provided calculations and expressed uncertainty about their results, while others have acknowledged the complexity of the problem. There is a mix of attempts to clarify relationships between variables and to confirm the correctness of derived expressions.

Contextual Notes

Participants are working under the assumption that the disk rolls without slipping, and there is a focus on the energy conservation principle. The discussion reflects a collaborative effort to understand the dynamics involved without reaching a definitive conclusion.

NathanLeduc1
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Homework Statement


A solid disk of mass m and radius R rolls without slipping with a velocity v. Assuming it doesn't slip, how far vertically will it roll up an incline?

Homework Equations


I=0.5mr2
E=0.5Iω2
KE=0.5mv2
PE=mgh

The Attempt at a Solution


I'm thinking that we need to find the height h when the kinetic energy is converted to potential energy. So:
0.5Iω2+mv2=mgh
0.5*0.5mr2ω2+mv2=mgh
0.25r2ω2+v2=gh
h=(0.25r2ω2+v2)/g
Is that right? I feel weird because I still have ω in there.
 
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NathanLeduc1 said:

Homework Statement


A solid disk of mass m and radius R rolls without slipping with a velocity v. Assuming it doesn't slip, how far vertically will it roll up an incline?

Homework Equations


I=0.5mr2
E=0.5Iω2
KE=0.5mv2
PE=mgh

The Attempt at a Solution


I'm thinking that we need to find the height h when the kinetic energy is converted to potential energy. So:
0.5Iω2+mv2=mgh
0.5*0.5mr2ω2+mv2=mgh
0.25r2ω2+v2=gh
h=(0.25r2ω2+v2)/g
Is that right? I feel weird because I still have ω in there.
What's the relationship between v and ω ?
 
Ah, either you're a genius or I'm dumb. Probably both. Thank you.

I got a final answer of (1.2*v^2)/g = h.
 
Oops, 1.25... ((5/4)(v^2))/g = h
 
NathanLeduc1 said:
Ah, either you're a genius or I'm dumb. Probably both. Thank you.
Probably neither.

I considered a lengthier reply to your Original Post, but then though I'd see what you could do with a fairly subtle hint/question. From that, you completed the exercise. I commend you for that.

You might be surprised at how many people need to be led by the nose, step-by-step to an answer.

I got a final answer of (1.2*v^2)/g = h.
 

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