(a) How much of this initial kinetic energy isrotational? 1 J (b) What is the sp

Question

(a) How much of this initial kinetic energy isrotational?
1 J

(b) What is the speed of the center of mass of the sphere at theinitial position?
2 m/s (c) What is its total kinetic energy now?
3 J

(d) What is the speed of its center of mass now?
4 m/s

Explanation / Answer

let the angular velocity is V=*R I=(2/5)*m*R^2 =>m=0.38 kg a, we have Ek=m*V^2/2+I*^2/2 Ek=m*^2*R^2/2+(2/5)*m*R^2*^2/2=0.7*m*R^2*^2 =>m*R^2*^2=Ek/0.7=60/0.7=85.71 J rotational initial kinetic energy is Ekr=(2/5)*m*R^2*^2/2=17.14 J b, V=*R=15.018 m/s c, Ek=60-m*g*H=60-0.38*9.8*1=56.276 J d, =>V=56.276/(0.7*0.38)=14.545 m/s

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