- #1
physicos
- 46
- 1
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 ?
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 ?