Solid sphere Kinetic Energy problem

[pfunk22]

Homework Statement

A solid sphere is released from rest at the top of an incline of height H and angle 30°. The sphere then rolls down the incline without slipping until it reaches the bottom of the incline, at which point the speed of the center-of-mass of the sphere is found to be 65 cm/s.

What is the value of the height H?

Homework Equations

conservation of energy

KEi + REi + PEi = KEf + REi +PEf

PE=mgh
RE= 1/2*I*w^2
KE= 1/2*m*v^2
where I= 2/5*m*r^2
and v=w*r
w=omega
r=radius
m=mass
v=velocity

The Attempt at a Solution

apparently this is supposed to be solved without mass or the radius of the sphere.
but i can't get all those variables to cancel any help would be awesome.

mgh=1/2*m*(w*r)^2 + 1/2*(2/5mr^2)*(v/r)^2

 

[IBY]

Firstly, how did you set up the conservation of energy?
Secondly, did you use the fourth and fifth relevant equation you listed in order to substitute?

 

[pfunk22]

As

PEi = KE(linear)f + KE(rotational)f

and ended up with

mgh=1/2*m*(w*r)^2 + 1/2*(2/5mr^2)*(v/r)^2

 

[IBY]

The kinetic energy term lies the problem. You don't want to end up with neither w nor r, so don't replace v!

 

[pfunk22]

Thank you so much..this was really bugging me...ended up with h= 3.02cm.

 

[IBY]

Seems right to me.