Answer :
Final answer:
The banking angle θ for a race car to navigate a turn at 103 mi/h without the aid of friction can be calculated using the formula tan(θ) = (v2)/(gr). To find the additional radial force required at 175 mi/h, we use the centripetal force equation and subtract the force provided by banking.
Explanation:
The first step is to convert all the quantities in uniform units. So, convert the speed from mi/h to ft/sec for convenience. Using the formula for the banking angle for a car rounding a turn without the aid of friction:
tan(θ) = (v2)/(gr)
where 'v' is the speed (103 mi/h converted to ft/sec), 'g' is the acceleration due to gravity (32.2 ft/s2) and 'r' is the radius of turn (1000 ft). Next, to find the additional radial force required at 175 mi/h, we use the equation for centripetal force:
F = mv2/r
where 'm' is the mass of the car (3.20 x 10³ lb converted to slugs), 'v' is the speed (175 mi/h converted to ft/sec) and 'r' is the radius of the turn (1000 ft). Subtracting the force provided by the banking angle gives the additional force required.
Learn more about Banking Angle and Radial Force here:
https://brainly.com/question/14501553
#SPJ11