# Finding a Vertical Force given friction and a horizontal force

• crazyog
In summary, the problem involves a box with a weight of 50 N being pulled horizontally with a force of 10 N. To start the box moving, a vertical force must also be applied. The coefficient of static friction is 0.4 and the question asks for the smallest vertical force needed for the box to move. By using the equation F(s)= mu(s)*normal force, it can be determined that the normal force must be equal to 25 N to overcome the force of friction and start the box moving.

#### 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?

## 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!

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
?

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

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!

## What is the formula for finding a vertical force given friction and a horizontal force?

The formula for finding a vertical force in this scenario is: Fv = μFn - Fh, where Fv is the vertical force, μ is the coefficient of friction, Fn is the normal force, and Fh is the horizontal force.

## How do I determine the coefficient of friction in this equation?

The coefficient of friction can be determined experimentally by measuring the force required to overcome friction and calculating it using the formula μ = Ff/Fn, where μ is the coefficient of friction, Ff is the force of friction, and Fn is the normal force.

## What is the normal force and how is it related to the vertical force?

The normal force is the perpendicular force exerted by a surface on an object in contact with it. In this equation, the normal force is used to calculate the vertical force by multiplying it by the coefficient of friction and subtracting the horizontal force.

## Can the vertical force be negative in this scenario?

Yes, the vertical force can be negative if the horizontal force is greater than the product of the coefficient of friction and the normal force. This would indicate that the object is moving in the opposite direction of the applied horizontal force.

## How does the magnitude of the frictional force affect the vertical force?

The magnitude of the frictional force, represented by the coefficient of friction, directly affects the vertical force. The higher the coefficient of friction, the greater the vertical force needed to overcome it and maintain motion in the horizontal direction.