Pencil urgent help

Question

A pencil leans against a wall so that its sharpened edge rests against the vertical surface of the wall and its eraser rests on the floor. The center of mass of the pencil is 9 cm from the end of the eraser and 11 cm from the tip of the lead. The coefficient of static friction between the eraser and the floor is 0.80. What is the minimum angle ø the pencil can make with the floor such that it does not slip?

Answer 1

For this problem, the friction from the eraser on the floor must be capable of generating torque on the pencil great enough to balance the torque created by gravity pulling on the center of gravity of the pencil. Make a diagram, showing all of the forces, then calculate the torques as a function of the angel. When the angle becomes low enough that the normal force (which goes down as the angle goes down) combined with the coefficient of static friction cannot generate enough torque to counter that created by gravity, then the pencil will slide,.