Question

A solid sphere rolls in released from rest and rolls down an incline plane, which is 2.0 m long and inclined at a 30° angle from the horizontal. (a) Find its speed at the bottom of the incline. (Remember that the kinetic energy in rolling motion is the translational kinetic energy ½ Mv2 of the center, plus the rotational K.E. ½ Iω2 about the center. Also remember that v = ωr if the sphere rolls without slipping.) (b) Find the fraction of the final K.E. which is rotational. (c) Assuming that the acceleration is constant (which it is), use kinematic equations to find the acceleration of the sphere down the incline.

Answer 1

Solution la From Conservation of mechanical energy mg L sino = mv 2 +2 I w2 => Mg Lisin200= £ mv2txş MR X v2 Oos-mgh = MV2++ mv24 - R2 = I MV2 V = Jos xte ga 7 9,8X200 500x = 3.74 m/s v =[3174 ] mij (b) fraction = mv2 I MV2 = 2 fraction = 1/2 (① a= masin 300 (M+ 1/R2) - mgroo5o.5mg - (M + m) / m. = syos g _ 215x968 7 7 = 315 m/s2 3.5 m2 a=