A solid sphere of mass 0.50 kg rests on a horizontal surface. The coefficient of static friction between the sphere and the surface is 2/7 . Determine the maximum horizontal force that can be applied at the highest point of the sphere such that it does not slip on the surface.

Step-by-step solution

Let the applied horizontal force at the highest point be F and the force of static friction at the contact point be f , acting in the forward direction. For translational motion, Newton's second law gives: F + f = ma For rotational motion about the center of mass, the torque equation is: F R - f R = I For a solid sphere, the moment of inertia is I = 2 5 m R^2 . For pure rolling (no slipping), the acceleration of the center of mass is a = R . Substituting these into the torque equation: F R - f R = ( 2 5 m R^2 ) ( a