A simple pendulum consisting of a bob of mass m attached to a string of length L is held such that the string is horizontal. It is then released from rest. What is the kinetic energy of the bob at the instant the string makes an angle with the downward vertical?

Step-by-step solution

Let the lowest point of the pendulum's path be the reference level for potential energy. When the string is horizontal, the height of the bob above the lowest point is L . When the string makes an angle with the downward vertical, the height of the bob above the lowest point is L - L . The vertical distance the bob has fallen is L - (L - L ) = L . According to the principle of conservation of mechanical energy, the loss in gravitational potential energy is equal to the gain in kinetic energy. Loss in potential ener