A simple pendulum consists of a 50 cm long string attached to a 100 g ball. The ball is drawn aside until the string forms an angle of 37^ with the vertical, and is subsequently released. Determine the tension in the string when the bob reaches its lowest position.

Step-by-step solution

Given m = 100 g = 0.1 kg , L = 50 cm = 0.5 m , and = 37^ . The height descended by the bob from its initial position to the lowest point is: h = L - L = L(1 - 37^ ) Substituting the values, we get: h = 0.5 (1 - 4 5 ) = 0.5 0.2 = 0.1 m Using the principle of conservation of mechanical energy, the velocity v at the lowest point is given by: 1 2 mv^2 = mgh v^2 = 2gh Taking g = 10 m/s ^2 , we have: v^2 = 2 10 0.1 = 2 m ^2/ s ^2 At the lowest position, the net force towards the center provides the necessary centripetal