Consider a simple pendulum with a bob of mass m that has an amplitude of ₀ . Determine the tension in the string when the bob reaches its extreme position.

Step-by-step solution

Let the length of the pendulum be L . At the extreme position, the angle made by the string with the vertical is ₀ . The velocity of the bob at the extreme position is zero, so the centripetal acceleration is v^2/L = 0 . The forces acting on the bob along the direction of the string are the tension T towards the support and the component of weight mg ₀ away from the support. Applying Newton's second law in the radial direction: T - mg ₀ = mv^2 L Since v = 0 at the extreme position: T - mg ₀ = 0 T = mg ₀