Truck brakes can fail if they get too hot. In some mountainous areas, ramps of l

Question

Truck brakes can fail if they get too hot. In some mountainous areas, ramps of loose gravel are constructed to stop runaway trucks that have lost their brakes. The combination of a slight upward slope and a large coefficient of rolling friction as the truck tires sink into the gravel brings the truck safely to a halt. Suppose a gravel ramp slopes upward at 6.0 and the coefficient of rolling friction is 0.40.

Use work and energy to find the length of a ramp that will stop a

15,000 kg truck that enters the ramp at 30 m/s .

Explanation / Answer

Given that mass of the truck is m = 15000 kg

coefficient of friction is ? = 0.40

speed v = 30 m/s

K.E = 1/2 mv^2

          = 1/2 * 15000 kg * ( 30 m/s)^2

          = 6.74*10^6 J

K.E = F * d

F = mg sin? + ? mgcos ?

d = K.E / ( mg sin? + ? mgcos ?)

     = 6.74*10^6 J / ( 15000 kg * 9.8 sin (6) + 0.4 * 15000 *9.8 cos (6)

     = 41.71 m

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