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 0.30. How long the ramp should be to stop a truck of 15000 kg having a speed of 35 m/s.

Question

Jayce Juarez

Mathematics

3 July, 13:33

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 0.30. How long the ramp should be to stop a truck of 15000 kg having a speed of 35 m/s.

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Answers (1)

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Susan Kline · Answer 1

Kinetic engery = - 1/2mv^2

Work = Fd

Combine:

-1/2mv^2 - Fd = 0

-1/2mv^2 = (0.30*15000*9.81*cos (6)) d = 0

Multiply both sides by 2:

v^2 = 2d (0.30*9.81*cos (6))

Solve for d:

d=v^2 / 2 (0.30*9.81*cos96))

v = speed:

d = 35^2 / 2*0.30 * 9.81 * cos (6)

d = 1225 / 5.85376

d = 209.27 meters. Round answer as needed.