Hollow Rolling Sphere up incline

[jjd101]

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

 

[Harrisonized]

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.

 

[jjd101]

I did this and got E=10.66, now do i set that equal to mgh to find height?

 

[Harrisonized]

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.

 

[jjd101]

okay, but how do i account for the incline?

 

[Harrisonized]

[PLAIN]http://img194.imageshack.us/img194/2649/220pxtrigonometrytriang.png [Broken]

...

 

[jjd101]

i know what a triangle looks like but i don't know how to deal with energy and an incline

 

[Harrisonized]

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.