Question

SOLVE THIS ASAP TO RATE HIGH!!

Problem 13.103 The pilot of the airplane executes a vertical loop which in part follows the path of a cardioid, TE200 (1 + cos @mwhere is in radians. His speed at A is a constant Up = 85 m/s. He has a mass of 86 kg Hint To determine the time derivatives necessary to calculate the acceleration components ar and de, take the first and second time derivatives of T=200 (1 + cose). Then for further information, use v Part A Determine the vertical reaction the seat of the plane exerts on the pilot when the plane is at A Express your answer to three significant figures and include the appropriate units. Figure 1 of 1 + - 200 (+ doe die N Value Units Submit Request Answer

Answer 1

Path of the cardioids executed by airplane: r = 200(1+cose) m = 200(1+ cos 0°)m = 400 m Path of cardioids executed by airplane: d (0) = [20061 + dt 1 = 200 (1+cos e)m d [200(1+cos8)m] dt r = 200(-sin e = 200 (-sin 0°)(0) = 0 m/s Using the equation: d dt r = 200(-sin e (r) = (2006- sin )(0)] = 200[-8 sin 8 – o cose] O=09 = 200[ -e sin ° – coso] =-20002

Magnitude of velocity: (",)? =p2 +(10) (85 m/s)? = ()²+(400 mx 0)? = 0.212 rad/s Angular acceleration of aeroplane is, O=0 r =-20002 =-200(0.212 rad/s) =-8.988 m/s2 Radial acceleration of airplane is, a =r-102 =-8.988 m/s2 – (400 m)(0.212 rad/s)? = -26.96 m/s2 Equilibrium motion in radial direction of the airplane cardioids path: EF, = -ma, N-mg= -ma, IN N-(86 kg)(9.8 m/s?) =-(86 kg)(-26.96 m/s2) 1 kg.m/s? N= 3.16 KN Vertical reaction by the seal of the plane on pilot is 3.16 kN