Question

A it takes 144 N of force to move a 56 kg block that is surface with friction. What is the coefficient of static friction for the surface?

Answer 1

Applying the Newton’s Second Law of Motion, we get (at the moment when the block begins to move the acceleration is zero):

$$\sum F_x=ma_x=0,$$ $$F_{appl}-F_{s.fr.}=0,$$ $$F_{appl}=F_{s.fr.}=\mu_sN=\mu_smg.$$

From this formula we can find the coefficient of static friction for the surface:

$$\mu_s=\dfrac{F_{appl}}{mg}=\dfrac{144\ N}{56\ kg\cdot 9.8\ \dfrac{m}{s^2}}=0.26$$

Answer:

$\mu_s=0.26$