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Finding a Vertical Force given friction and a horizontal force

  1. Jun 3, 2008 #1
    [SOLVED] Finding a Vertical Force given friction and a horizontal force

    1. The problem statement, all variables and given/known data
    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)


    2. Relevant 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

    3. 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!
     
  2. jcsd
  3. Jun 3, 2008 #2

    nicksauce

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    Maybe write it out clealry for yourself. What are the forces in each direction? What are the equations of constraint?
     
  4. Jun 3, 2008 #3
    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
    ????
     
  5. Jun 3, 2008 #4

    nicksauce

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    Why mg = n for the vertical? What about the new vertical force for which you are trying to solve?
     
  6. Jun 3, 2008 #5
    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!
     
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