A block having a mass m is pressed against a wall by a hand exerting a force F inclined at an angle θ to the wall, as shown. The coefficient of static friction is μ. We shall investigate the question of how large the force F must be in order to keep the block from sliding along the wall.
(a) Find the smallest value of F that will keep the block from sliding downwards.
(b) Find the largest value of F that will keep the block from sliding upwards.
Show that if μ is greater than cotθ, then no matter how strong the force is, the block will not slide upwards.