You want to design an oval racetrack such that 3200 lb racecars can round the tu

Question

You want to design an oval racetrack such that 3200 lb racecars can round the turns of radius 1000ft at 102 mi/h without the aid of friction. You estimate that when elements like down force and grip in the tires are considered the cars will round the turns at a maximum of 175 mi/h. Find the banking angle theta necessary for the racecars to navigate these turns at 102 mi/h and without the aid of friction. This banking and radius are very close to the actual turn data at Daytona International Speedway where 3200 lb stock cars travel around the turns at about 175 mi/h. What additional radial force is necessary to hold the racecar on the track at 175 mi/h?

Explanation / Answer

v = (22/15)*102 = 149.6 ft/sec
For no friction, = arctan[v²/(R*g)] =arctan[(149.6)^2/1000x9.8]= 66.35 degree

Anet = [(v²/R + g²] = 33.2 ft/sec²
Af = Anet*sin = 17.93 ft/sec²
Ff = m*Af = (3200/32.2)*Af = 1781.9 lb along the slope.
Fr = Ff*cos = 1500 lb

ans- Banking angle theeta is 66.35 degree

Ans-Additional radial force is 1500lb

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