Use the figure to answer the next problem. A spring of negligible mass and spring constant k is attached to the wall on one end,and the other end is attached to the center of mass axis of a solid sphere of mass m and radius r.The spring is stretched a distance A from equilibrium and let go.The sphere rolls freely on a smooth surface.
-What is the linear kinetic energy when the sphere is at the equilibrium position?
E)undetermined

Question

Use the figure to answer the next problem. A spring of negligible mass and spring constant k is attached to the wall on one end,and the other end is attached to the center of mass axis of a solid sphere of mass m and radius r.The spring is stretched a distance A from equilibrium and let go.The sphere rolls freely on a smooth surface. 
-What is the linear kinetic energy when the sphere is at the equilibrium position?
E)undetermined

Quizplus · Accepted Answer

At the equilibrium position, the spring is at its natural length and the sphere is at rest. Therefore, all of the initial potential energy stored in the spring is converted to kinetic energy. The potential energy stored in the spring is given by U = 0.5kA^2. 
The total energy of the system is conserved, so at the equilibrium position, all of this potential energy is converted to the linear kinetic energy of the center of mass of the sphere: 
0.5kA^2 = 0.5mv^2 
v^2 = kA^2/m 
The linear kinetic energy of the center of mass is given by K = 0.5mv^2 = 0.5kA^2. Substituting the given values, we have K = 0.5(2/5mr^2)(A^2/r^2) = 1/5mA^2. Therefore, choice B is correct.

Use the Figure to Answer the Next Problem