What is the Maximum Height a Rolling Marble Reaches on a Rough Hill?

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Homework Help Overview

The problem involves a solid uniform marble rolling without slipping towards a hill, with the goal of determining the maximum height it can reach based on its initial speed. The context is rooted in the principles of conservation of energy, particularly relating to rotational and linear motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of conservation of energy, equating potential energy and kinetic energy. There is an exploration of the relationship between the marble's initial speed and the height it can achieve. Some participants express uncertainty about rearranging equations and eliminating variables related to the moment of inertia.

Discussion Status

The discussion is ongoing, with participants providing guidance on rearranging equations and questioning the assumptions made about the variables involved. There is a recognition of the need to clarify how the final height is expressed in relation to the initial speed and other parameters.

Contextual Notes

Participants note that the problem requires a specific height in meters and that the solution must not include the initial speed as a variable, raising questions about the completeness of the problem statement provided.

raiderIV
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Homework Statement


A solid uniform marble is rolling without slipping when it approaches the base of a hill with a speed v0.

Find the maximum height above the base that this marble will reach if the hill is rough enough to prevent slipping.


Homework Equations


Since there is no slipping I can use the conservation of energy

mgh = .5mv2 + .5Iw2

and i end up with the equation

v02 = 10gh/7


The Attempt at a Solution



I have no idea where to go from here, so if someone might be willing to give me a point in the correct direction, it would be most appreciated.
 
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raiderIV said:

Homework Statement


A solid uniform marble is rolling without slipping when it approaches the base of a hill with a speed v0.

Find the maximum height above the base that this marble will reach if the hill is rough enough to prevent slipping.


Homework Equations


Since there is no slipping I can use the conservation of energy

mgh = .5mv2 + .5Iw2

and i end up with the equation

v02 = 10gh/7


The Attempt at a Solution



I have no idea where to go from here, so if someone might be willing to give me a point in the correct direction, it would be most appreciated.

You seem pretty much done. You equated the final PE with the initial total KE (linear and rotational), and the final PE has the final height in it that you are asked to solve for. Just re-arrange your final equation.


EDIT -- actually I'm not sure I understand your final equation. You can eliminate the I in the initial equation by using the definition of a sphere's I in terms of its mass and radius. It does seem like your final answer will still have variables in it for m, R and Vo.
 
berkeman said:
You seem pretty much done. You equated the final PE with the initial total KE (linear and rotational), and the final PE has the final height in it that you are asked to solve for. Just re-arrange your final equation.EDIT -- actually I'm not sure I understand your final equation. You can eliminate the I in the initial equation by using the definition of a sphere's I in terms of its mass and radius. It does seem like your final answer will still have variables in it for m, R and Vo.
The problem is, that the final solution is asking for a set height in meters. I tried plugging in 9.81 for gravity and solving for h and leaving v0 in there, but to no avail (Its a computer system that i need to input the answers to, and it just tells me that the answer does not use v0 in it). I just don't know if there is someway to find h other than what i am aware of.
 
raiderIV said:
The problem is, that the final solution is asking for a set height in meters. I tried plugging in 9.81 for gravity and solving for h and leaving v0 in there, but to no avail (Its a computer system that i need to input the answers to, and it just tells me that the answer does not use v0 in it). I just don't know if there is someway to find h other than what i am aware of.

The final height will depend on Vo. Right? Maybe not on the mass, but for sure on the Vo. What are you not posting about the original problem statement?
 

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