High Banked Turn

A stock car of mass \(1400\text{ kg} \) is racing around a speedway with banked turns. The car and turn are shown in the figures below.

  • Its wheelbase is a rectangle with width \(170\text{ cm}\), and its center of mass is centered in that rectangular wheelbase.
  • With the car sitting on the level road, its center of mass is \(50\text{ cm}\) above the road surface.
  • The car has a velocity through the turn of \(40 \text{ m/s}\).
  • The turn radius is \(100\text{ m}\).
  • The bank angle of the track surface in the turn is \(30^\circ\).

Find the combined force normal to the track surface exerted on the right side tires.

Express your positive answer (in Newtons) as the force on the right front plus the force on the right rear.

Details and Assumptions:

  • Take \(g = 10\text{ m/sec}^2 \).
  • Ignore possible aerodynamic forces.
  • Ignore possible tangential accelerations due to throttle or brake.
  • Ignore possible center of mass movement due to suspension movement.
  • Ignore possible gyroscopic effects from rotating mass in engine or wheels.
  • The car is turning left.

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