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

[raiderIV]

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.

 

[berkeman]

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.

 

[raiderIV]

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.

 

[berkeman]

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?