Finding a Vertical Force given friction and a horizontal force

[crazyog]

[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?
(answer: 25 N)

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 I am 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]

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

 

[crazyog]

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]

Why mg = n for the vertical? What about the new vertical force for which you are trying to solve?

 

[crazyog]

Oh I see,I think I understand, if the normal force is 25 then it will be
10 -(.4*25)=0
so a force of 25 is able to overcome the force of friction.

thanks!