Sphere rolling up a ramp No mass given

[mightymango]

Sphere rolling up a ramp.. No mass given!

Homework Statement

A solid sphere of radius 20cm, has a velocity of 5.0m/s and is moving on a surface with just enough friction to allow it to spin. It rolls up an incline of 30 degrees. Calculate the distance rolled before it comes to rest on the incline.

Homework Equations

PE + KE = PE
mgh + .5mv^2 = mgh

The Attempt at a Solution

I cancel out m, and plug in: (9.81)(0) + (1/2)(5.0)^2 = (9.81)(h). h is 1.27, so I use trig to find the length of ramp, which is 2.54 m.
However, I feel like I'm missing something crucial in this answer, and none of the choices match.

 

[PeterO]

Homework Statement

A solid sphere of radius 20cm, has a velocity of 5.0m/s and is moving on a surface with just enough friction to allow it to spin. It rolls up an incline of 30 degrees. Calculate the distance rolled before it comes to rest on the incline.

Homework Equations

PE + KE = PE
mgh + .5mv^2 = mgh

The Attempt at a Solution

I cancel out m, and plug in: (9.81)(0) + (1/2)(5.0)^2 = (9.81)(h). h is 1.27, so I use trig to find the length of ramp, which is 2.54 m.
However, I feel like I'm missing something crucial in this answer, and none of the choices match.

Are you accounting for the the fact this rather large sphere is spinning?

 

[rock.freak667]

Your KE would be split into rotational KE + translational KE such that:

KE = ½Iω²+ ½mv² and you know that v=rω

 

[mightymango]

Ok. So I accounted for the spin of the sphere.

New equation is (1/2)(2/5)mr^2w^2 + (1/2)mv^2 = mgh

m's cancel. I plugged in .2m for r, 5 for v, and 25 for w using v=rw. After isolating h, I multiplied by 2 to find the distance on the ramp. However, I'm still not getting the right answer... Not sure what I'm doing wrong.

 

[rock.freak667]

What value did you get for h and what is the given answer?