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

The coefficient of kinetic friction
`\mu_k =  0.724`

Step-by-step 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 =  (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`