Chapter 13.6, Problem 103P

The pilot of the airplane executes a vertical loop which in part follows the path of a cardioid, r = 200(1 + cos θ) m, where θ is in radians. If his speed at A is a constant v_p = 85 m/s. determine the vertical reaction the seat of the plane exerts on the pilot when the plane is at A. He has a mass of 80 kg. Hint: To determine the time derivatives necessary to calculate the acceleration components ar and a_θ, take the first and second time derivatives of r = 200(1 + cos θ). Then, for further information, use Eq. 12-26 to determine $\stackrel{\dot{}}{\theta }$.