Question

For an object of given mass pushed against a vertical surface, and given a coefficient of static friction, calculate the horizontal force necessary to prevent vertical motion

Answer 1

As long as the given mass does not begin to move in any direction on the vertical surface ex. Wall and just stays static on the wall under pressure in the same position, there is no role of friction while it stays there! It is only when the given mass starts to move in a certain direction, that friction will be experienced in the opposite direction.

And greater the verticallly compressive force on the given mass is during its horizontal movement on the wall, greater will be the friction experienced in the opposite direction horizontally with respect to the wall's surface! Also note that you need a horizontal vector to make the mass move. So as you press the given mass against the vertical surface with your vertical compressive force, you may end up giving the mass an additional horizontal force either inadvertently or advertently which will make the mass start to move on the surface of the wall in a certain direction. Friction will be experienced then and the frictional force can be calculated as the vertical force on the book or mass times the coefficient of friction of the surface of the wall, just like if it were on the ground. On the ground it will generally be the mass weight that will be the vertically downward force that you will take into account, and the coefficient of friction on the ground.