# Finding a Vertical Force given friction and a horizontal force

[SOLVED] Finding a Vertical Force given friction and a horizontal force

## Homework Statement

Problem:
A box with a weight of 50 N rests on a horizontal surface. A person pulls horizontally on it with a force of 10 N and it does not move. To start it moving, a second person pulls vertically upward on the box. If mu(s) =0.4 (coefficient of static friction) what is the smallest vertical force for which the box moves?

## Homework Equations

I think I might use F(s)= mu(s)*normal force
because if (mu*n) > F(s) then the object will move (?)
but then im not really sure what to do with the 10N

## The Attempt at a Solution

My original thoughts would be =0.4*50N will give you 20N for the force of friction but that does not give me a vertical force
If I were to just think of the vertical force as the normal force then it would just be 50N..?
I'm confused, any help is greatly appreciated, thanks!

nicksauce
Homework Helper
Maybe write it out clealry for yourself. What are the forces in each direction? What are the equations of constraint?

So for the horizontal force is it: 10- fk = ma where fk is equal to mu*n
10-(.4*50) = ma
-10 = ma
and for the vertical mg= n
mg = mg
????

nicksauce