Question

If the coefficient of static friction is 0.23 and the coefficient of kinematics friction is 0.18 what force is required to start a 8.6 kg object moving ?

Answer 1

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

$$\sum F_x = ma_x = 0,$$ $$F_{appl} - F_{s.fr.} = 0,$$ $$F_{appl} = F_{s.fr.} = \mu_s N = \mu_s mg,$$

here, $F_{appl}$ is the applied force required to start a 8.6 kg object to move, $F_{s.fr.}$ is the force of static friction, $\mu_s = 0.23$ is the coefficient of static friction, $N$ is the normal force, $m = 8.6 kg$ is the mass of the object and $g$ is the acceleration due to gravity.

Then, we get:

$$F_{appl} = \mu_s mg = 0.23 \cdot 8.6 kg \cdot 9.8 \dfrac{m}{s^2} = 19.4 N.$$

Answer:

$F_{appl} = 19.4 N.$