Answer to Question #169757 in Mechanics | Relativity for Mae

Question

you are working as a letter sorter in the Post office. Postal regulations require that employees' footwear must have a minimum coefficient of static friction of 0.5 on a specified tile surface. You are wearing athletic shoes for which you do not know the coefficient of static friction. In order to determine the coefficient, you imagine that there is an emergency and start running across the room. You have a co-worker time you, and find that you can begin at rest and move 4.23 m in 1.20s. If you try to move faster that this, your feet slip. Assuming your acceleration is constant, does your footwear qualify for the postal regulation?

Answer 1

Let's solve this exercise in part, let's start by finding with kinematics the acceleration of man

$y = v₀ t + \frac{1}{2} a t²$

as it starts from rest the initial velocity is zero

$y = \frac{1}{2}a t²$

$a = \large\frac{2y}{t^2}$

$a =\frac{2 * 4.38}{1.21^2}$

$a = 6.46 m / s²$

Now let's use Newton's second law,

Axis y

N - W = 0

N = W

N = m g

Axis x

on this axis, the man exerts a backward force and by the law of action and reaction the floor exerts a forward force of the same magnitude, this forward force is the friction force.

     $f_r = m a$

the friction force has an expression

     $f_r = \mu N$

let's substitute

   $μmg = ma$

   $μ = a / g$

let's calculate

   $μ = 6.46 / 9.8$

   $μ = 0.66$