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2 years ago

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You may have noticed runaway truck lanes while driving in the mountains. These gravel-filled lanes are designed to stop trucks t

hat 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.

1 answer:

kati45 [8]2 years ago

6 0

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

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

=> $\Delta KE = 0.5 * m * 22.6^2$

=> $\Delta KE = 255.38m$

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

=> $255.38 = 352.8 * \mu_k$

=> $\mu_k = 0.724$

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