Question

A Runaway Truck Name: 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 resistance as the truck tires sink into the loose gravel brings the truck safely to a halt. Suppose such 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 35 m/s (75 mph).

Answer 1

mg The free body diagram of the truck is shown. The truck is not allowed to move normal to the most o & mgcosa ramp, the net force in this direction must be zero - N-mg coso =0 -> N= mg cosa The rolling resistance on the truck is For = MoN = Mg mg cosa The component of gravitational force along the hamp is F = masina Net force is - F= F + Fg - Hy mg cosa + mgsina The net work done on the truck is Ws - Fd - - mgd (Mocos + sina) where work done by the net force is negative

because net force is in opposite direction to the displacement of the truck Applying work energy theorem W = Kaine - Kinitial In the final state, the truck comes to rest so the final Kinetic energy is zero -mgd (ulycose + sino) - zmus o da za Sine) d = (35m/s) 2 2(9.8 m/s2) (0.4 6056°rsin 6°) d=124m