Question

A solid sphere of weight 35.5 N rolls up an incline with an inclination angle of 25.0

Answer 1

the moment of inertia of the sphere, I = 2/5mR^2
the weight of the object W = mg
from this the mass of the object, m = w/g
mass, m = 35.5/9.8 = 3.6224 kg
(a)

The K.E of the sphere , K.E = 1/2mv^2 + 1/2Iw^2
                                      K.E = 1/2mV^2 + 1/5mV^2
                                             = 0.7mV^2
                                             = 0.7*3.6224*(4.5)^2
                                              = 51.35 N.m
the kinetic energy of the sphere is 51.35 N.m.

(b) According to conservation of energy,

      mgh = K.E ===> mg(dsin?) = K.E ===> 35.5*sin25^o*d = 51.35

Therefore, the required distance is, d = 3.42 m