Question

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.

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 lbSource(s):Free body diagram 
My 'cheat sheet' of physics formulae