Question

You may have noticed runaway truck lanes while driving in the mountains. These gravel-filled lanes are designed to stop trucks that have lost their brakes on mountain grades. Typically, such a lane is horizontal (if possible) and about 36.0 m36.0 m long. Think of the ground as exerting a frictional drag force on the truck. A truck enters a typical runaway lane with a speed of 50.5 mph50.5 mph ( 22.6 m/s22.6 m/s ). Use the work-energy theorem to find the minimum coefficient of kinetic friction between the truck and the lane to be able to stop the truck.

Answer 1

Answer:

The  coefficient of kinetic friction  $\mu_k = 0.724$

Explanation:

From the question we are told that

   The  length of the lane is  $l = 36.0 \ m$

    The speed of the truck is  $v = 22.6\ m/s$

     

Generally from the work-energy theorem we have that  

    $\Delta KE = N * \mu_k * l$

Here N  is the normal force acting on the truck which is mathematically represented as

     $\Delta KE$ is the change in kinetic energy which is mathematically represented as

        $\Delta KE = \frac{1}{2} * m * v^2$

=>     $\Delta KE = 0.5 * m * 22.6^2$

=>      $\Delta KE = 255.38m$

        $255.38m = m * 9.8 * \mu_k * 36.0$

=>     $255.38 = 352.8 * \mu_k$

=>   $\mu_k = 0.724$