As shown in the figure, a long board with mass m and length L is placed on a smooth horizontal plane, and an object with mass m (regarded as a particle) rushes up to the board from the left end at a certain initial speed. If the long board is fixed, the object just stops at the right end of the board. If the long board is not fixed, the maximum distance that the object can slide on the board after it rushes up to the board is () A. LB. 3L4C. L4D. L2

As shown in the figure, a long board with mass m and length L is placed on a smooth horizontal plane, and an object with mass m (regarded as a particle) rushes up to the board from the left end at a certain initial speed. If the long board is fixed, the object just stops at the right end of the board. If the long board is not fixed, the maximum distance that the object can slide on the board after it rushes up to the board is () A. LB. 3L4C. L4D. L2

If the long board is fixed, the block just stops at the right end of the board. For the sliding process of the small slider, the kinetic energy theorem is used to draw the equation: 0-fl = 0-12mv20 ① If the long board is not fixed, after the block rushes onto the board, the block decelerates to the right and the board accelerates. Finally, both of them move at a constant speed. The resultant force of the external force on the system is zero and the momentum is conserved. The right direction is defined as the positive direction. According to the momentum conservation of the system, MV0 = (M + m) v ② The energy conservation of the system is: FL ′ = 12mv20-12 (M + m) v2 ③ From the above formula, l ′ = L2