A pencil initially stands vertically on a horizontal surface. A sight push causes it to fall

over.

a$.$ Show that horizontal component of the reaction force $$ can be expressed as a

function of the tilt $$ according to $=3/4(32)$

b$.$ From the above expression, determine the range of angles the pencil will tend to

slide to the left or right.

c$.$ What forces produces $?$

Treat the pencil as a thin uniform rod of length $.$