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The coefficient of static friction between the road and the tires on a racecar is 0.50. Calculate the speed that will put the car on the verge of sliding as it rounds a level curve of 35 meters radius.

a) 33.24 m/s
b) 42.43 m/s
c) 55.68 m/s
d) 29.21 m/s

User Lovlesh
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1 Answer

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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.

User Zamphatta
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