Use work and energy to find the length of a ramp that will stop a 15,000 kg truc

Question

Use work and energy to find the length of a ramp that will stop a 15,000 kg truck that enters the ramp at 31 m/s .

Truck brakes can fail fthey 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 0.33.

Explanation / Answer

Given that; mass of the truck is m = 15000 kg

coefficient of friction is u = 0.33

speed v = 31 m/s

theta @ = 6.0 degree

K.E = 1/2* m*v^2

= 1/2 * 15000 * ( 31)^2

= 7.21*10^6 J

K.E = F * d

F = mg sin@ + u*mg cos@

d = K.E / ( mg sin@ + u*mg cos@)

= 7.21*10^6 J / ( 15000 kg * 9.8 sin (6) + 0.33 * 15000 *9.8 cos (6)

= 1310 m

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