Map sapling learning You want to design an oval racetrack such that 3200 lb race

Question

Map sapling learning You want to design an oval racetrack such that 3200 lb racecars can round the turns of radius 1000 ft at 96 milh 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 milh. Find the banking angle 0 necessary for the racecars to navigate these turns at 96 milh and without the aid of friction. Number 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 milh. What additional radial force is necessary to hold the racecar on the track at 175 mih? Number

Explanation / Answer

Mass of racecar, m = 3200 lb = 1451.5 kg

Turn radius, R = 1000 ft = 304.8 m

Banking speed when friction is unaccounted, v = 96 mi/h = 42.916 m/s

Banking speed when friction is accounted, vf = 175 mi/h = 78.232 m/s

Without friction, the maximum velocity a car can achieve on a banked turn is:

v = [gR(tan )]1/2

=> tan = v2/gR = 42.9162/(9.81*304.8) = 0.616

=> = tan-1(0.616) = 31.63o

Let F be the frictional force & N be the normal reaction acting on the racecar. Following equations hold:

Fcos + Nsin = mvf2/R

Fsin + mg = Ncos

Solving for F, we get,

F = m(vf2cos/R - gsin)

=> F = 1451.5[78.2322*cos(31.63o)/304.8 - 9.81*sin(31.63o)] = 17347.94 N

So, additional radial force needed to hold the racecar on the track at 175 mi/h is:

Fcos = 17347.94 * cos31.63o = 14770.9 N

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