A cart of mass M rests on a frictionless horizontal surface, and a pendulum bob of mass m hangs from the roof of the cart as shown in the figure. After the string breaks, the bob falls to the floor, experiences several collisions on the floor, and eventually lands in a small slot made in the floor. The horizontal distance between the string and the slot is L . Determine the displacement of the cart during this proces

Step-by-step solution

Since there is no external force acting on the system (cart and bob) in the horizontal direction, the horizontal position of the center of mass of the system remains stationary. Let x be the displacement of the cart relative to the ground. The displacement of the bob relative to the cart is L . Therefore, the displacement of the bob relative to the ground is x + L . Using the principle of conservation of the center of mass position: M x_ M + m x_ m = 0 M x + m (x + L) = 0 (M + m) x + mL = 0 x = - mL M + m The negat