You wish to make a simple amusement park ride in which a steel-wheeled roller-coaster car travels down one long slope, where rolling friction is negligible, and later slows to a stop through kinetic friction between the roller coaster's locked wheels sliding along a horizontal plastic (polystyrene) track. Assume the roller-coaster car (filled with passengers) has a mass of 759.5 kg and starts 83.4 m above the ground. (a) Calculate how fast the car is going when it reaches the bottom of the hill. m/s (b) How much does the thermal energy of the system change during the stopping motion of the car? (C) If the car stops in 236.00 m, what is the coefficient kinetic friction between the wheels and the plastic stopping track?

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You wish to make a simple amusement park ride in which a steel-wheeled roller-coaster car travels down one long slope, where rolling friction is negligible, and later slows to a stop through kinetic friction between the roller coaster's locked
wheels sliding along a horizontal plastic (polystyrene) track. Assume the roller-coaster car (filled with passengers) has a mass of 759.5 kg and starts 83.4 m above the ground.
(a) Calculate how fast the car is going when it reaches the bottom of the hill.
m/s
(b) How much does the thermal energy of the system change during the stopping motion of the car?
(c) If the car stops in 236.00 m, what is the coefficient of kinetic friction between the wheels and the plastic stopping track?
Transcribed Image Text:You wish to make a simple amusement park ride in which a steel-wheeled roller-coaster car travels down one long slope, where rolling friction is negligible, and later slows to a stop through kinetic friction between the roller coaster's locked wheels sliding along a horizontal plastic (polystyrene) track. Assume the roller-coaster car (filled with passengers) has a mass of 759.5 kg and starts 83.4 m above the ground. (a) Calculate how fast the car is going when it reaches the bottom of the hill. m/s (b) How much does the thermal energy of the system change during the stopping motion of the car? (c) If the car stops in 236.00 m, what is the coefficient of kinetic friction between the wheels and the plastic stopping track?
Expert Solution
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The car is at a height of 83.4 m from the ground, with a mass of 759.5 kgAt this height, the potential energy of the car will beP.E=mghP.E=759.5×9.8×83.4P.E=620754.54 J

As the car starts coming down the track, this potential energy will start getting converted into its kinetic energyAs it reaches the bottom, the potential energy of the car will become zero,and it will have some maximum kinetic energyFrom law of conservation of energy,Energy at bottom=energy at topEnergy at the bottom=12mv2v is the velocity of the car at the bottom

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