Max Distance Up Ramp for Rotating Sphere

[physicos]

A uniform solid sphere of mass M and radius R is rolling without sliding along a level plane with a speed v = 2.30 m/s when it encounters a ramp that is at an angle θ = 27.6° above the horizontal. Find the maximum distance that the sphere travels up the ramp if :
1-
the ramp is frictionless, so the sphere continues to rotate with its initial angular speed until it reaches its maximum height.
→ I used : Ki+Ui=Kf+Uf
and concluded that Ki=7/10* m*v² =mglsinθ
so l = (7/10 *m*v²)/(mg*sinθ).

is it true ?
2-
the ramp has enough friction to prevent the sphere from sliding so that both the linear and rotational motion stop (instantaneously).
→ I concluded the same as the first case : means l = (7/10 *m*v²)/(mg*sinθ).
is it correct ?

 

[vela]

A uniform solid sphere of mass M and radius R is rolling without sliding along a level plane with a speed v = 2.30 m/s when it encounters a ramp that is at an angle θ = 27.6° above the horizontal. Find the maximum distance that the sphere travels up the ramp if :
1-
the ramp is frictionless, so the sphere continues to rotate with its initial angular speed until it reaches its maximum height.
→ I used : Ki+Ui=Kf+Uf
and concluded that Ki=7/10* m*v² =mglsinθ
so l = (7/10 *m*v²)/(mg*sinθ).

is it true ?

Nope.

2-
the ramp has enough friction to prevent the sphere from sliding so that both the linear and rotational motion stop (instantaneously).
→ I concluded the same as the first case : means l = (7/10 *m*v²)/(mg*sinθ).
is it correct ?

It turns out this one is correct. Obviously the two cases are different, so you need to figure out where you messed up in the first part of the problem.

 

[paisiello2]

Where did the 7/10 come from?

Does the sphere have rotational kinetic energy?

 

[physicos]

The sphere has both rotational and transitional kinetic energy

 

[physicos]

Nope.It turns out this one is correct. Obviously the two cases are different, so you need to figure out where you messed up in the first part of the problem.

FOR THE FIRST CASE :

Kf+Uf=Ki+Ui
so 1/2m*v²_f+1/2*I*w²+mg*l*sinθ=1/2*m*v²+1/2*I*w²
so It becomes : mg*l*sinθ=1/2*m*v²so l = v²/2*g*sinθ

Is it correct now ?

 

[paisiello2]

That part looks right to me.