Final answer:
The kinetic energy of a solid sphere rolling without slipping on a horizontal surface is the sum of its translational and rotational kinetic energy. The total kinetic energy for such a moving sphere is calculated to be 7/10 mvcm2, where m is the mass of the sphere and vcm is the velocity of the sphere's center of mass.
Step-by-step explanation:
An object that rolls without slipping on a horizontal surface has both translational and rotational motion, thus its total kinetic energy is the sum of the translational kinetic energy (due to the motion of the center of mass) and the rotational kinetic energy (about the center of mass).
The translational kinetic energy (TKE) is calculated using TKE = 1/2 mvcm2, where m is the mass of the sphere and vcm is the velocity of the center of mass. For the rotational kinetic energy (RKE), it is calculated using RKE = 1/2 Icmω2, where Icm is the rotational inertia of the sphere about its center or Icm = 2/5 mr2, and ω is the angular velocity related to the translational velocity by vcm = rω.
For a solid sphere rolling without slipping, the total kinetic energy (KE) is the sum of translational and rotational kinetic energies: KE = TKE + RKE = 1/2 mvcm2 + 1/2 (2/5 mr2)(ω2). Substituting vcm = rω gives us KE = 7/10 mvcm2.