Hollow Rolling Sphere up incline

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Homework Help Overview

The problem involves a hollow sphere rolling up an incline, with specific parameters including mass, diameter, and initial velocity. The inquiry focuses on determining how far the sphere travels up the incline before stopping and reversing direction, while ignoring friction.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the moment of inertia and energy conservation principles, noting the relationship between kinetic energy and gravitational potential energy. Questions arise regarding how to set up the equations and account for the incline in calculations.

Discussion Status

Some participants have provided insights into the energy equations involved, while others express uncertainty about how to apply these concepts to the incline. There is an ongoing exploration of the relationship between forces, energy, and the geometry of the incline.

Contextual Notes

Participants mention assumptions such as rolling without slipping and the need to consider both translational and rotational motion. There is also a note about the importance of not calculating raw numbers too early in the problem-solving process.

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Homework Statement


An 800 g, 40.0 cm diameter hollow sphere is rolling along at 4 m/s when it comes to a 25 degree incline. Ignoring any friction, how far along the incline does it roll before it stops and reverses its direction?



Homework Equations


rolling momentum
motion equations

The Attempt at a Solution


i have no idea where to start
 
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http://en.wikipedia.org/wiki/List_of_moments_of_inertia

Moment of inertia of a hollow sphere is I = 2/3 mr2 (according to Wikipedia).

The kinetic energy of a system is the sum of its translational and rotational motion.

E = 1/2 mv2 + 1/2 Iω2

Of course, this has to be equal to the energy lost from going up that incline, which is mgh.

Also note that there is the assumption that the sphere is rolling without slipping.

If you're studying calculus and you run into problems, take the derivative. If you're studying linear algebra and you run into problems, row-reduce. When you're studying kinetics and you run into problems, examine the energy of the system.
 
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I did this and got E=10.66, now do i set that equal to mgh to find height?
 


It's rolling UP an incline. Go figure.

And fyi, you should never calculate for raw numbers until the very end of a problem. It's bad practice.
 
okay, but how do i account for the incline?
 
[PLAIN]http://img194.imageshack.us/img194/2649/220pxtrigonometrytriang.png

...
 
Last edited by a moderator:
i know what a triangle looks like but i don't know how to deal with energy and an incline
 
mg is a force. h is a height. Forces are vectors. You can put them on triangles.

I recommend reviewing energy in a system that only involves translational motion. This is a pretty basic concept and if you don't understand it, you shouldn't be studying rotational motion.
 

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