请完成这道题---**Extraction Content:** **Question Number:** 15. (18分) **Question Stem:** 如图所示，足够长的斜面固定在水平地面上，薄木板 D 恰能靠在斜面上保持静止，两者上端对齐。斜面的左边有一水平平台，平台上 MN 段粗糙，M 点左边光滑，M 点与四分之一圆弧轨道 C 相切，其末端与平台相切于 M 点。两个相同的滑块 A、B 在 MN 段，它们之间压缩一轻质弹簧，弹簧与 A、B 不栓接，同时由静止释放 A、B，当弹簧恢复原长时，滑块 A 恰从 M 点滑上圆弧轨道 C，滑块 B 恰从 N 点水平飞出，并且无碰撞地落在木板 D 上端。已知弹簧初始压缩量 Δx = 0.5 m，滑块 A、B 均可视为质点，它们的质量均为 m₁ = 1 kg，圆弧轨道 C 的质量 m₂ = 3 kg，圆弧面光滑，木板足够长且质量也为 m₁ = 1 kg，其上端与 N 点的竖直距离 h = 0.45 m，滑块 A、B 与平台 MN 段之间的动摩擦因数 μ₀ = 0.5，滑块 B 与木板 D 之间的动摩擦因数 μ₁ = 0.875，斜面倾角 θ = 37°，重力加速度 g = 10 m/s²，sin 37° = 0.6，不计空气阻力。 **Translation of Question Stem:** As shown in the figure, a sufficiently long inclined plane is fixed on a horizontal ground, and a thin wooden board D can just rest on the inclined plane and stay still, with their upper ends aligned. To the left of the inclined plane is a horizontal platform. The section MN of the platform is rough, and the section to the left of point M is smooth. Point M is tangent to a quarter-circle track C, and its end is tangent to the platform at point M. Two identical blocks A and B are on the section MN, with a compressed light spring between them. The spring is not attached to A or B. Blocks A and B are released from rest simultaneously. When the spring returns to its original length, block A just slides onto the quarter-circle track C from point M, and block B flies horizontally from point N, landing on the upper end of the wooden board D without collision. It is known that the initial compression of the spring is Δx = 0.5 m. Blocks A and B can be regarded as point masses, and their masses are both m₁ = 1 kg. The mass of the quarter-circle track C is m₂ = 3 kg. The surface of the circular track is smooth. The wooden board is sufficiently long and its mass is also m₁ = 1 kg. The vertical distance from the upper end of C (point O) to point N is h = 0.45 m. The coefficient of kinetic friction between blocks A, B and the platform section MN is μ₀ = 0.5. The coefficient of kinetic friction between block B and wooden board D is μ₁ = 0.875. The angle of inclination of the inclined plane is θ = 37°, and the acceleration due to gravity is g = 10 m/s². sin 37° = 0.6, cos 37° = 0.8. Neglect air resistance. **Sub-questions:** (1) 求弹簧释放的弹性势能 Ep； (2) 从滑块 B 与木板 D 接触到它们共速的过程中，求它们之间因摩擦产生的热量 Q； (3) 若滑块 A 恰能运动到圆弧轨道 C 的最高点且从滑上圆弧轨道到最高点用时 t = 2 s，求该过程圆弧轨道 C 的位移大小 x_CO。 **Translation of Sub-questions:** (1) Find the elastic potential energy Ep released by the spring. (2) Find the heat Q generated due to friction between block B and wooden board D during the process from contact until they reach a common velocity. (3) If block A can just reach the highest point of the quarter-circle track C and takes time t = 2 s from sliding onto the circular track to the highest point, find the magnitude of the displacement x_CO of the quarter-circle track C during this process. **Diagram Description:** * **Type:** Schematic diagram illustrating a physics problem setup. * **Main Elements:** * **Inclined Plane (D):** A right-angled triangle shape representing an inclined plane. Its base is on the horizontal ground, and it makes an angle θ with the horizontal. A thin rectangular board labeled D is placed on the inclined plane. * **Horizontal Platform:** A horizontal surface extends to the left of the inclined plane. * **Sections on Platform:** The platform is divided into a rough section labeled MN (indicated by wavy lines) and a smooth section to the left of M. * **Points:** Points M and N are marked on the horizontal platform, defining the rough section. Point O is marked above M, connected by a dashed vertical line. * **Quarter-circle Track (C):** A curved track labeled C, shaped as a quarter circle, is placed to the left of M. It is tangent to the platform at M. Point O is the center of this quarter circle, located directly above M. Block A is shown on this track. * **Blocks (A and B):** Blocks labeled A and B are shown initially on the MN section of the platform. Later, block A is shown on track C, and block B is shown in the air, flying horizontally from N towards the inclined plane D. * **Spring:** A compressed spring is implied to be between A and B initially. * **Height:** A vertical dashed line indicates the height h from point N to point O. * **Angle:** The angle of inclination of the inclined plane D is labeled θ. * **Relative Position and Direction:** The inclined plane D is on the right. The horizontal platform is to its left. The rough section MN is on the platform, with the smooth section to the left of M. The quarter-circle track C is located above and to the left of M, with its center O directly above M. Point N is to the right of M on the platform. Block B flies horizontally from N towards D. Block A moves along the track C from M. * **Labels and Annotations:** M, N, O, A, B, C, D, h, θ are labeled. Wavy lines indicate friction on MN. The base is indicated as a textured surface (ground). **Note:** The question specifies that wooden board D also has mass m₁ = 1 kg.