A simple pendulum of length 1 m has a bob of mass 100 g . If the bob has a speed of 1.4 m/s when the string makes an angle of 0.20 radian with the vertical, determine the tension in the string at this instant. You may use the approximations 1 - ^2/2 and for small .

Step-by-step solution

Given: Length of the pendulum, l = 1 m Mass of the bob, m = 100 g = 0.1 kg Speed of the bob, v = 1.4 m/s Angle with the vertical, = 0.20 rad Acceleration due to gravity, g = 9.8 m/s ^2 Using the small angle approximation for : 1 - ^2 2 = 1 - (0.20)^2 2 = 1 - 0.02 = 0.98 The forces acting on the bob along the radial direction are the tension T towards the pivot and the component of weight mg away from the pivot. The net force provides the necessary centripetal acceleration: T - mg = mv^2 l Rearranging for tension T