Question 25 of 27 Map t Sapling Learning nacmian learning You want to design an

Question

Question 25 of 27 Map t Sapling Learning nacmian learning You want to design an oval racetrack such that 3200 lb racecars can round the turns of radius 1000 ft at 105 miVh 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 min. Find the banking angle necessary for the racecars to navigate these tuns at 105 mi/h 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 cars travel around the turns at about 175 mi/h. What ádditional radial force is necessary to hold the racecar on the track at 175 mi/h? Number

Explanation / Answer

The question is actually asking for banking angle.

We know that

tan(theta) = v^2/rg

v = 105 mi/h = 46.94 m/s ; r = 1000 ft = 304.8 m

tan(theta) = 46.94^2/304.8 x 9.81 = 0.73688

theta = tan^-1(0.73688) = 36.4 deg

Hence, theta = 36.4 deg

Since the car is following a curved path,

F = mv^2/R ; m = 1451.5 kg ; v = 175 mi/h = 78.23 m/s

F = 1451.5 x 78.23^2/304.8 = 29144 N

When it moves with former speed

F' = 1451.5 x 46.94^2/304.8 = 10492 N

Fadd = 29144 - 10492 = 18652 N

Hence, F = 18652 N

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