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

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.<br /><br />Given information:<br />- Mass of the roller coaster train: 4768 kg<br />- Initial speed of the roller coaster train: 17.1 m/s<br />- Final speed of the roller coaster train: 2.2 m/s<br />- Distance over which the train is decelerated: 13.6 m<br /><br />Step 1: Calculate the initial and final kinetic energies of the roller coaster train.<br />Initial kinetic energy (KE_initial) = (1/2) × m × v_initial^2<br />KE_initial = (1/2) × 4768 kg × (17.1 m/s)^2<br />KE_initial = 1,234,000 J<br /><br />Final kinetic energy (KE_final) = (1/2) × m × v_final^2<br />KE_final = (1/2) × 4768 kg × (2.2 m/s)^2<br />KE_final = 12,000 J<br /><br />Step 2: Calculate the change in kinetic energy.<br />ΔKE = KE_final - KE_initial<br />ΔKE = 12,000 J - 1,234,000 J<br />ΔKE = -1,222,000 J<br /><br />Step 3: Calculate the work done on the roller coaster train.<br />Work done (W) = ΔKE<br />W = -1,222,000 J<br /><br />Step 4: Calculate the retarding force acting on the roller coaster train.<br />Work done (W) = Force (F) × Distance (d)<br />-1,222,000 J = F × 13.6 m<br />F = -89,852 N<br /><br />The negative sign indicates that the force is in the opposite direction of the motion of the roller coaster train, which is the retarding force.<br /><br />Therefore, the retarding force acting on the roller coaster train is 89,852 N.