An engineer wants to design an oval racetrack such that 3.20 x 10³ lb racecars can round the exactly 1000 ft radius turns at 103 mi/h without the aid of friction. She estimates that the cars will round the turns at a maximum of 175 mi/h.

a) Find the banking angle [tex]\theta[/tex] necessary for the race cars to navigate the turns at 103 mi/h without the aid of friction.

b) What additional radial force is necessary to prevent a race car from drifting on the curve at 175 mi/h?

Question

05-06-2025
Physics

High School

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An engineer wants to design an oval racetrack such that 3.20 x 10³ lb racecars can round the exactly 1000 ft radius turns at 103 mi/h without the aid of friction. She estimates that the cars will round the turns at a maximum of 175 mi/h.

a) Find the banking angle [tex]\theta[/tex] necessary for the race cars to navigate the turns at 103 mi/h without the aid of friction.

b) What additional radial force is necessary to prevent a race car from drifting on the curve at 175 mi/h?

Answer :

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shreya236se shreya236se · Answer 1 · 2024-12-18T08:31:38-05:00

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:

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