What is the maximum static friction of my shoe against the wood board?

[colemansmith]

Homework Statement

Basically, I need to find the maximum static friction of my shoe against a wood board.
I discovered that after increasing the slope of the board, my shoe slipped at an angle of 29.33 degrees. (using tan theta = O/A) O being 42.7 cm and A being 76 cm. The shoe has a weight of 5 Newtons. I calculated the mass of the shoe by using the formula Fg = mg, where Fg = 5, and g = 9.8. Thus: 5 = m(9.8) which equals 0.51.
A quick recap:
theta = 29.33 degrees
weight (Fg) = 5
mass = 0.51

I am supposed to find the Maximum Static Friction of my shoe against the wood. I do not[b/] know the co-efficients of either (we are not supposed to use them from out text's)

Homework Equations

tan theta = O/A

Fg = mg

Ff = u Fn (u is miu or the frictional co-efficient)

The Attempt at a Solution

Here is a diagram depicting my work so far.

I am basically stuck. Any help would be great (formulas, tips, anything)

Thanks guys and gals

Coleman.

 

[BishopUser]

Your diagram misses a coordinate system. Try to think of a coordinate system that would make the problem easier. Specifically, a coordinate system in which one or more of the forces acted entirely in the X or Y direction. Once you break the forces into their x/y components you can then use the equations you listed.

 

[nlightner]

Hello Coleman,

Based on the information provided, we can calculate the maximum static friction using the formula Ff = uFn, where Ff is the maximum static friction, u is the frictional coefficient, and Fn is the normal force.

To find the normal force, we can use the formula Fn = mgcos(theta), where m is the mass of the shoe and g is the acceleration due to gravity.

Substituting the values we have, we get:
Fn = (0.51)(9.8)cos(29.33) = 4.44 N

Now, we can use this value of Fn to calculate the maximum static friction:
Ff = uFn
Ff = u(4.44)
Ff = 4.44u

Since we do not know the frictional coefficient, we can rearrange the equation to solve for u:
u = Ff/4.44

So, the maximum static friction of your shoe against the wood board is 4.44u, where u is the coefficient of friction.

I hope this helps! Let me know if you have any other questions.

Best, (Scientist)