我是一个高三的学生，请你详细的给我讲讲这道题。特别是把运动的过程和受力的关系讲清楚。---**Extracted Content:** **Question 15.** (16 分) **Problem Description:** 如图甲所示，物块 b 静止在足够长的固定斜面上，t=0 时刻将质量 m₁=1kg 的物块 a 从物块 b 上方斜面上某处由静止释放，t=8s 时 a 与 b 发生第一次碰撞，t=14s 时 a 与 b 发生第二次碰撞。0~14s 内物块 a 的速度 v 随时间 t 变化的图像如图乙所示，每次碰撞均为弹性碰撞且碰撞时间极短，取重力加速度 g=10m/s²。求: (1) 斜面倾角的正弦值 sinθ; (2) 物块 b 的质量 m₂; (3) 物块 a 开始运动到停下的整个过程中，物块 b 与斜面间因摩擦产生的热量。 **Translation of Problem Description:** As shown in Figure 甲, block b is stationary on a sufficiently long fixed inclined plane. At time t=0, a block a with mass m₁=1kg is released from rest from a certain point on the inclined plane above block b. At t=8s, a and b have their first collision, and at t=14s, a and b have their second collision. The graph of block a's velocity v versus time t from 0~14s is shown in Figure 乙. Each collision is an elastic collision and the collision time is extremely short. Take the acceleration due to gravity g=10m/s². Calculate: (1) The sine value of the inclined angle sinθ; (2) The mass of block b, m₂; (3) The heat generated by friction between block b and the incline during the entire process from when block a starts moving until it stops. **Figures:** **Figure 甲 (Jia):** Type: Diagram Description: Shows an inclined plane with angle θ between the plane and a horizontal dashed line. Two rectangular blocks, labeled 'b' and 'a', are on the inclined plane. Block 'a' is positioned higher up the incline than block 'b'. **Figure 乙 (Yi):** Type: Line chart (Velocity-Time Graph) Main Elements: * X-axis: t / s (time in seconds) * Y-axis: v / (m⋅s⁻¹) (velocity in meters per second) * Origin: (0,0) * Graph segments: * From t=0 to t=8s: A straight line from (0,0) to (8,8). Represents block 'a' accelerating down the slope. * At t=8s: Velocity changes abruptly from 8 m/s to -6 m/s. Represents the first collision. * From t=8s to t=10s: A straight line from (8,-6) to (10,0). Represents block 'a' moving up the slope and decelerating to rest. * From t=10s to t=14s: A straight line from (10,0) to (14,4). Represents block 'a' moving down the slope and accelerating. * Labeled points and values: (0,0), (8,8), (8,-6), (10,0), (14,4). The values 8, -6 are marked on the y-axis. The values 8, 10, 14 are marked on the x-axis. Dotted lines connect the points at t=8, 10, 14 to the respective axes and the graph line. **Given Values:** * Mass of block a: m₁ = 1kg * Acceleration due to gravity: g = 10m/s² * First collision time: t = 8s * Second collision time: t = 14s * Collisions are elastic and extremely short. **Questions:** (1) sinθ (2) m₂ (3) Heat generated by friction between block b and the incline during the entire process from when block a starts moving until it stops.