19. A circular race track has a radius of 159 m. If the centripetal force acting on a 65.0 kg cyclist is 416 N, what is the frequency of the cyclist? (A) 1.27times 10^-3Hz (B) 3.20times 10^-3Hz (C) 1.01times 10^-2Hz (D) 1.01times 10^-1Hz

Here's how to solve this problem:1. **Understand the relationship between centripetal force, mass, velocity, and radius:** The formula for centripetal force (Fc) is: Fc = mv²/r where: * m is the mass * v is the velocity * r is the radius2. **Relate velocity to frequency:** The cyclist is traveling in a circle. The velocity (v) can be expressed in terms of the circumference of the circle and the frequency (f): v = 2πrf where: * r is the radius * f is the frequency (number of revolutions per second)3. **Substitute and solve for frequency:** Substitute the expression for velocity (v) into the centripetal force equation: Fc = m(2πrf)²/r = 4π²mr²f²/r = 4π²mrf² Now, solve for frequency (f): f² = Fc / (4π²mr) f = √[Fc / (4π²mr)]4. **Plug in the given values:** f = √[416 N / (4π²(65.0 kg)(159 m))] f = √[416 / (4π²(65)(159))] ≈ 0.0101 Hz5. **Match the answer:** The closest answer is (C) Hz.Therefore, the correct answer is (C).Final Answer: The final answer is