A simple pendulum of length L is released from rest from a horizontal position. At its lowest point, the pendulum bob collides with a rigid vertical wall. After rebounding, the pendulum swings back up to a maximum angle with the vertical, such that = 0.64 . The percentage loss of mechanical energy during the collision and the coefficient of restitution between the bob and the wall, respectively, are :

Step-by-step solution

Let the mass of the pendulum bob be m . The initial mechanical energy of the bob relative to the lowest point is: E_i = mgL After the collision, the bob rebounds and reaches a maximum angle with the vertical. The maximum height reached by the bob is: h = L(1 - ) = L(1 - 0.64) = 0.36L The mechanical energy of the bob just after the collision is: E_f = mgh = 0.36mgL The loss in mechanical energy during the collision is: E = E_i - E_f = mgL - 0.36mgL = 0.64mgL The percentage loss of mechanical energy is: % loss = ( E