A crate of weight Fg is pushed by a force P on a horizontal floor. (a) If the coefficient of static friction is μ s and P is directed at angle θ below the horizontal, show that the minimum value of P that will move the
crate is given by
P = usFgSecθ / (1 - usTanθ)
(b) Find the minimum value of P that can produce motion when μ s = 0.400,
If the angle were 68.2° or more, the expression for P would go to infinity and motion would become impossible.
The Attempt at a Solution
I was able to figure out how to get to P, but I cannot figure out how to find the minimum value of P. I am assuming that if they want the minimum value of P, theta would be equal to 0, since all of the force would be put along the horizontal. I am not sure where exactly to go from there though.