You want to design an oval racetrack such that 3200 lb racecars can round the turns of radius 1000 ft at 1.00 _ 102 mi/h without the aid of friction. You estimate that when elements like downforce and grip in the tires are considered the cars will round the turns at a maximum of 175 mi/h. Find the banking angle necessary for the racecars to navigate these turns at 1.00 _ 102 mi/h and without the aid of friction or other forces.

Question

Physics

Skylar French

11 April, 11:08

You want to design an oval racetrack such that 3200 lb racecars can round the turns of radius 1000 ft at 1.00 _ 102 mi/h without the aid of friction. You estimate that when elements like downforce and grip in the tires are considered the cars will round the turns at a maximum of 175 mi/h. Find the banking angle necessary for the racecars to navigate these turns at 1.00 _ 102 mi/h and without the aid of friction or other forces.

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Jaylon Williams · Answer 1

v = (22/15) * 98 = 143.7 ft/sec

For no friction, Θ = arctan[v² / (R*g) ] = 32.68°

Anet = √[ (v²/R + g²] = 33.2 ft/sec²

Af = Anet*sinΘ = 17.93 ft/sec²

Ff = m*Af = (3200/32.2) * Af = 1781.9 lb along the slope.

Fr = Ff*cosΘ = 1500 lb Source (s) : Free body diagram

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