Answer to Question #168924 in Mechanics | Relativity for April

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 1.20 s. If you try to move faster than this, your feet slip. Assuming your acceleration

is constant, does your footwear qualify for the postal regulation?

Answer 1

Let's first find the final velocity of the letter sorter:

$$d=\dfrac{1}{2}(v_0+v)t,$$ $$v=\dfrac{2d}{t}=\dfrac{2\cdot4.23\ m}{1.2\ s}=7.05\ \dfrac{m}{s}.$$

Then, we can find the acceleration of the letter sorter:

$$a=\dfrac{v-v_0}{t}=\dfrac{7.05\ \dfrac{m}{s}-0}{1.2\ s}=5.87\ \dfrac{m}{s^2}.$$

Let's apply the Newton's Second Law of Motion:

$$F_{fr}=ma,$$ $$\mu_smg=ma,$$ $$\mu_s=\dfrac{a}{g}=\dfrac{5.87\ \dfrac{m}{s^2}}{9.8\ \dfrac{m}{s^2}}=0.6.$$

According to the calculations, employees’ footwear have a coefficient of static friction of 0.6 and the minimum required  coefficient of static friction is 0.5. Therefore, the footwear qualify for the postal regulation.