Chapter 5, Problem 74RPP

Texas Motor Speedway On October 28, 2000 Gil de Ferran set the single-lap average speed record for the then-named California Speedway—241.428 mi /h. The following year, on April 29, 2001, the Championship Auto Racing Teams (CART) organization canceled the inaugural Firestone Firehawk 600 race at the Texas Motor Speedway 2 hours before it was to start. During practice, drivers became dizzy when they reached speeds of more than 230 mph on the high-banked track The Texas Motor Speedway has turns banked at $24°$ above the horizontal. By comparison, turns on the Indianapolis Motor Speedway are banked at $9°$.

In qualifying runs for the race, 21 of 25 drivers complained of dizziness and disorientation They experienced accelerations of 5.5g (5.5 times $\text{9}{\text{.8 m/s}}^{\text{2}}$) that lasted for several seconds Such accelerations for such long time intervals have caused pilots to black out. Blood drains from their heads to their legs as they move in circles with their heads toward the center of the circle. CART felt that the track was unsafe for their drivers. The Texas Motor Speedway had tested the track with drivers before the race and thought it was safe The Texas Motor Speedway sued CART.

If the racecars had no help from friction, which expression below would describe the normal force of the track on the cars while traversing the $24°$ banked curves?

$\begin{array}{l}\text{a}\text{. }mg\cos 66°\hfill \\ \text{b}\text{. }mg\sin 66°\hfill \\ \text{c}\text{. }mg/\cos 66°\hfill \\ \text{d}\text{. }mg/\sin 66°\hfill \\ \text{e}\text{. None of these}\hfill \end{array}$