Question

An airplane accelerates uniformly from rest. A physicist passenger holds up a thin string of negligible mass to which she has tied her ring, which has a mass m. She notices that as the plane accelerates down the runway, the string makes an angle 0 with the vertical as shown above. 56. In the space below, draw a free-body diagram of the ring, showing and labeling all the forces present. (a)

Answer 1

(a) w rightarrow is the weight of the ring (= mg) 'm' is the mass of the string T rightarrow tension in the string ma rightarrow pseudo force on the ring which is opposite to the direction of motion of the plane. 'a' is the acceleration of the plane. (b) acceleration (a) = v - u/t = 65 m/s - 0 m/s/30 s = 13/6 m/s^2. length (s) = ut + 1/2 at^2 = 0 + 1/2 times (13/6 m/s^2) times (30s)^2 = 975 m (c) From the Fig. horizontal forces Sigma F_x = 0 rightwardsdoublearrow T sin theta - ma = 0 rightwardsdoublearrow T din theta - ma__(1) Vertical forces Sigma F_y = 0 rightwardsdoublearrow T cos theta - mg = 0 rightwardsdoublearrow T cos theta = mg___(2) rightwardsdoublearrow tan theta a/g = 13/6 m/s^2/9.8 m/s^2 = 0.22109 rightwardsdoublearrow theta = 12.47 degree. (d) Kinetic energy of the plane (k) = 1/2 Mv^2 The value of 'v' is given 65 m/s but the mass of the plane (M) is needed.