Final answer:
The maximum speed that a racecar with a coefficient of static friction of 0.50 can round a level curve of 35 meters radius without sliding is calculated using the formula for centripetal force, yielding an answer of 42.43 m/s.
Step-by-step explanation:
To find the speed at which a racecar would be on the verge of sliding as it rounds a level curve, you can use the formula for centripetal force which needs to be provided by static friction: Fc = μsmg = mv2/r. Here, Fc is the centripetal force required to keep the car moving in a circle, μs is the coefficient of static friction, m is the mass of the racecar, g is the acceleration due to gravity, v is the velocity, and r is the radius of the curve.
By rearranging the formula to solve for v, and inputting the coefficient of static friction (μs = 0.50) and the radius of the curve (r = 35 m), the equation becomes v = √(μsgr). Plugging the values g = 9.81 m/s2 and substituting the given values, we find that v = √(0.50 * 9.81 m/s2 * 35 m).
By calculating this expression, we determine the speed that will put the car on the verge of sliding. A suitable answer from the options provided based on this calculation is b) 42.43 m/s as the speed amid those options where the car would be on the verge of sliding.