# What is your brother’s static coefficient of friction and his kinetic (sliding) coefficient of friction?

## Your younger brother (who happens to weigh 480 Newtons) is in your room again and he won’t leave. You have to drag him out of your room while he is kicking and screaming. It takes you 310 Newtons of force to start dragging him. Once he is moving it only takes 195 Newtons.

Feb 20, 2017

The static coefficient is 0.65; the kinetic coefficient is 0.41

#### Explanation:

Start by considering the forces that act on your little brother. Gravity and the normal force of the floor are present, but as these act vertically (and little brother is not moving vertically) we can conclude that they cancel out, and are not a factor here.

Looking at horizontal forces, you are pulling with a force ${F}_{a}$, and friction opposes you with force ${F}_{f} = \mu {F}_{N} = \mu m g$, where $m g$ is the weight of your brother (480 N).

Your applied force must balance the force of friction, because your brother is not accelerating.

${F}_{a} = \mu m g$

To get him moving, the static coefficient applies:

$310 = {\mu}_{s} \left(480\right)$

${\mu}_{s} = \frac{310}{480} = 0.65$

Once he is moving, the kinetic coefficient applies:

$195 = {\mu}_{k} \left(480\right)$

${\mu}_{k} = \frac{195}{480} = 0.41$