Problemas
5. A 4768-kg roller coaster train full of riders approaches the loading dock at a speed of 17.1m/s It is that acts upon the roller coaster cars. abruptly decelerated to speed of 2.2m/s over a distance of 13.6 m Determine the retarding force
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Manuel
professionell · Tutor durante 6 años
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To determine the retarding force acting on the roller coaster train, we can use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.Given information:- Mass of the roller coaster train: 4768 kg- Initial speed of the roller coaster train: 17.1 m/s- Final speed of the roller coaster train: 2.2 m/s- Distance over which the train is decelerated: 13.6 mStep 1: Calculate the initial and final kinetic energies of the roller coaster train.Initial kinetic energy (KE_initial) = (1/2) × m × v_initial^2KE_initial = (1/2) × 4768 kg × (17.1 m/s)^2KE_initial = 1,234,000 JFinal kinetic energy (KE_final) = (1/2) × m × v_final^2KE_final = (1/2) × 4768 kg × (2.2 m/s)^2KE_final = 12,000 JStep 2: Calculate the change in kinetic energy.ΔKE = KE_final - KE_initialΔKE = 12,000 J - 1,234,000 JΔKE = -1,222,000 JStep 3: Calculate the work done on the roller coaster train.Work done (W) = ΔKEW = -1,222,000 JStep 4: Calculate the retarding force acting on the roller coaster train.Work done (W) = Force (F) × Distance (d)-1,222,000 J = F × 13.6 mF = -89,852 NThe negative sign indicates that the force is in the opposite direction of the motion of the roller coaster train, which is the retarding force.Therefore, the retarding force acting on the roller coaster train is 89,852 N.