Hopefully I can get help with this within the hour. You want to design an oval r
ID: 1278306 • Letter: H
Question
Hopefully I can get help with this within the hour.
You want to design an oval racetrack such that 3200 lb racecars can round the turns of radius 1000 ft at 105 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 105 mi/h and without the aid of friction or other forces.
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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?
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Explanation / Answer
tan theta = v2 / r g
105 mi/h = 46.94 m/s, r = 1000 ft = 304.8 mts
tan theta = (46.94)2 / (9.8 * 304.8)
tan theta = 0.738
theta = 36.41 deg
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F = m v2 / r
3200 lb = 3200 / 2.205 = 1451 kg
F = 1451.5 * (46.94)2 / (304.8)
= 10492.7 N = 1.049 * 104 N
force acts on body when moves with 175 mi/h
F = 1451.5 * (0.4470 * 175)2/(304.8)
F = 29140 N
additional force needed
= 18647 N = 1.86 * 104 N
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