Frictional Forces on a Wooden Crate with External Forces

[braydon]

having major issue with this question.

Homework Statement

a wooden crate of mass m= 60 kg sits on the horizontal surface. the coefficient of static friction between the block and the surface is u=0.5 . an external force P = 220 N, is also applied to the block in a direction parallel to the surface. Also an external force F is applied to the block in a direction perpendicular downwards to the surface.
A) if the force F = 40 N, what is the magnitude and direction of the frictional force that the surface exerts on the block?
B) what is the smallest force F, necessary to hold the block stationary on the surface?

variables
m = 60kg
P = 220N
U = 0.5

Homework Equations

equations
Fs<= U*Fn
F = ma
Fn = mg

The Attempt at a Solution

not sure on where to start for part a in this question. but was thinking for part b you let Ff = P so that
Ff<= U*Fn+f
Ff<= U*mg + f
220<= U*mg + f
and then rearrange to solve for f
am i on the right track for part b at least?

 

[haruspex]

Fn = mg

Not always, and not in this case.

Ff<= U*mg + f

Is f the same as the given F?
What you have written means F_f<=(U*mg)+f. Is that what you intended?