# Grantham PHY220 Week 2 Assignment Problem 8

### If a car is traveling at 50 m/s and then stops over 300 meters (while sliding), what is the coefficient of kinetic friction between the tires of the car and the road?

SOLUTION:

Draw the free-body diagram of the car

Consider the vertical direction

$\sum F_y=ma_y$

$F_N-mg=0$

$F_N=mg$

Consider the motion in the horizontal direction

Solve for the acceleration of the car.

$v^2=\left(v_0\right)^2+2a_x\Delta x$

$a_x=\frac{v^2-\left(v_0\right)^2}{2\Delta x}=\frac{0-50^2}{2\left(300\right)}=-4.17\:m/s^2$

Solve for the coefficient of kinetic friction

$\sum F_x=ma_x$

$-F_{fr}=ma_x$

$-\mu _kF_N=ma_x$

$\mu _k=\frac{ma_x}{-F_N}=\frac{m\:\left(-4.17\right)}{-m\left(9.80\right)}=\frac{4.17}{9.80}$

$\mu _k=0.43$