Deriving Formula to Solve Least Force Needed for Board Against Wall

[caseys]

In solving the problem of the least force needed to hold a board against the wall to prevent it from sliding down when the cof is known...the formula of F=mg/f was used to come up with the correct answer. Having found this formula in solving the problem it would be beneficial to also understand where this formula was derived from.

When looking at F=ma, a=gf, F=mg ...I just can not the way to derivating where the formula to solve the problem came from. Appreciate a boot in the correct direction...

 

[mezarashi]

I wouldn't normally call something like this a formula. It is "derived" from a free-body-analysis, in which the net forces acting on the ladder in the x and y directions must be equal to zero. They are a certain set of conditions for a given physical situation which can lead you to definite solutions such as the "formula" you mention.

If you draw such a diagram, you will see that at all times, for the ladder to remain in equilibrium, the reaction force from the wall will be equal to the frictional force, Ffrict = mg x f.

 

[caseys]

Thanks mezarashi...that is what I was thinking also of Ffrict = mg x f ... however, to come up for the correct answer for the problem it was neccesary to use mg/f ... just could not understand why the mg was divided by f rather than multiplied.