A simple pendulum is suspended from the ceiling of a car executing a turn of radius 10 m at a speed of 36 km/h . Determine the angle made by the pendulum's string with the vertical, given that this angle remains constant throughout the turn. Take g = 10 m/s ^2 .

Step-by-step solution

Given speed of the car, v = 36 km/h = 36 5 18 m/s = 10 m/s Radius of the turn, r = 10 m Centripetal acceleration of the car is a_c = v^2 r = 10^2 10 = 10 m/s ^2 In the frame of the car, the pendulum bob experiences a pseudo force horizontally outward and the gravitational force downwards. Balancing the forces in the frame of the car, with T as the tension in the string and as the angle it makes with the vertical: T = m a_c T = mg Dividing the two equations: = a_c g Substituting the values of a_c and g : = 10 10 = 1