Map cos Sapling Learning macrilan earring You want to design an oval racetrack s

Question

Map cos Sapling Learning macrilan earring You want to design an oval racetrack such that 3200 lb racecars can round the turns of radius 1000 ft at 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 6 necessary for the racecars to navigate these turns at 102 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 stock cars travel around theuns at about 175 mi/h. What additional radial force is necessary to hold the racecar on the track at 175 mi/h? Number

Explanation / Answer

We will use the conversion: 1 mi/hr = 0.4471 m/s

                                                      1 ft = 0.3048 m

                                                     1 lb = 0.4536 kg

So radius = 1000 ft = 1000 x 0.3048 m = 304.8 m

g*tan = V^2/r

tan = V^2/(r*g) = (0.4471*102)^2/(304.8*9.81) = 0.696

angle = arctan 0.696 = 34.82° (ans)

radial force F = m*V^2/r = (3200*0.4536)*(0.4471*102)^2/304.8 = 9904.16 N

@ 175 mph

radial force F1 = F*(175/102)^2 =29,153.68 N

additional force Fa = F1-F = 29,153.68 – 9904.16 = 19249.52 N (ans)

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