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.

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okpalawalter8 okpalawalter8 · Answer 1 · 2020-10-12T18:40:34+02:00

Answer:

The coefficient of kinetic friction [tex]\mu_k = 0.724[/tex]

Explanation:

From the question we are told that

The length of the lane is [tex]l = 36.0 \ m[/tex]

The speed of the truck is [tex]v = 22.6\ m/s[/tex]

Generally from the work-energy theorem we have that

[tex]\Delta KE = N * \mu_k * l[/tex]

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

[tex]\Delta KE[/tex] is the change in kinetic energy which is mathematically represented as

[tex]\Delta KE = \frac{1}{2} * m * v^2 [/tex]

=> [tex]\Delta KE = 0.5 * m * 22.6^2 [/tex]

=> [tex]\Delta KE = 255.38m [/tex]

[tex] 255.38m = m * 9.8 * \mu_k * 36.0 [/tex]

=> [tex] 255.38 = 352.8 * \mu_k [/tex]

=> [tex]\mu_k = 0.724[/tex]