Answer to Question #168133 in Physics for rgrgrgrgrg

Question

A 787-kg car is moving on a level road at 28 m/s and a constant retarding force stops it at a distance of 96. What is the minimum coefficient of friction between tires and roadway if this is to be possible? Assume the wheels are not locked, which case we are dealing with static friction - there's no sliding.

Answer 1

We can find the minimum coefficient of friction between tires and roadway from the work-kinetic energy theorem:

$$\Delta KE=W,$$ $$KE_f-KE_i=-F_{fr}d,$$ $$0-\dfrac{1}{2}mv_i^2=-\mu_smgd,$$ $$\mu_s=\dfrac{v_i^2}{2gd}=\dfrac{(28\ \dfrac{m}{s})^2}{2\cdot9.8\ \dfrac{m}{s^2}\cdot96\ m}=0.42$$