Chapter 13.7, Problem 112P

The pilot of an airplane executes a vertical loop which in part follows the path of a “four-leaved rose,” r = (–600 cos 2θ) ft, where θ is in radians. If his speed is a constant v_P = 80 ft/s, determine the vertical reaction the seat of the plane exerts on the pilot when the plane is at A. He weights 130 lb. Hint: To determine the time derivatives necessary to compute the acceleration components a_r and a₀, take the first and second time derivatives of r = 400(1 + cos θ). Then, for further information, use Eq. 12-26 to determine $\stackrel{\dot{}}{\theta }$. Also, take the time derivative of Eq. 12–26, noting that ${\stackrel{\dot{}}{\upsilon }}_P=0$ to determine $\stackrel{\dot{}}{\theta }$.