Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negotiating curves

QUESTION:

Problem 94GP

Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of 160 km/h (approximately 100 mi/h). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. (b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0° toward the center of the curve.