static friction co-efficient

yoleven

1. The problem statement, all variables and given/known data
from the free body diagram of a block resting on a flat surface, I am trying to derive the coefficient of static friction.



2. Relevant equations



3. The attempt at a solution
I have the definition of the coefficient as:
u_s=F_n/F_fr

But in my free body diagram i am pulling on the block, which resists with the F_fr
I have
[tex]\Sigma[/tex]F_x=0
F-F_fru_s=0
u_s=F/F_fr

My confusion is because if the definition of the coefficient is above, why don't I derive it when I observe my free body diagram of the block. What am I missing?
The forces in the x direction are my pulling force and the friction force that resists it * u_s
How do i get the weight of the block into my derived equation?

Doc Al

The weight of the block is Fn.

(If that's not what you're looking for, please state the complete problem exactly as it was given.)

yoleven

It is not a problem as such. I am trying to determine the coefficient of static friction u_s experimentally. Then, I am trying to determine if it is a function of surface area or of mass.
My experiment consists of a wooden block on a wooden flat surface. I am going to attach a spring scale and determine at what force the block overcomes the friction and moves.

In trying to determine u_s from my free body diagram I am having a little difficulty as I tried to explain.
From my free body diagram, if at equilibrium the forces in the x plane are zero, I get
F_pull-F_friction*u_s=0
but I don't see where I am getting the mass of the block to become part of my derived equation.

marlon

you also need to apply newton's second low in the Y-direction (vertical direction)

ma_y = F_normal - mg = 0

do you understand this equation ? Why is it equal to 0 ?

ps a_y is the component of the acceleration in the vertical direction
and F_normal is the normal force.

In this case, this is not gonna help you much because the table is horizontal.

marlon

Doc Al

What you should get is F_pull - F_friction = F_pull - μF_normal = 0.

yoleven

Thank you.

marlon

Nope,

F_pull=F_normal*u_s