A pendulum bob of mass 50 g hangs from the ceiling of an elevator. Determine the tension in the string given that the elevator is travelling downward with a deceleration of 1.2 m/s ^2 .

Step-by-step solution

Mass of the bob, m = 50 g = 0.05 kg The elevator is travelling downward with a deceleration, which means its acceleration is directed upwards. Let this acceleration be a = 1.2 m/s ^2 . Using Newton's second law with respect to the ground frame, the forces acting on the bob are the tension T upwards and the weight mg downwards. The equation of motion is: T - mg = ma T = m(g + a) Taking g = 9.8 m/s ^2 , we get: T = 0.05 (9.8 + 1.2) T = 0.05 11.0 T = 0.55 N