如何解这道题---**Extraction Content:**
**Question Stem:**
如图所示，一倾斜轨道 AB, 通过微小圆弧与水平轨道 BC 平滑连接, 水平轨道与一半径为 R=0.5m 的光滑圆弧轨道相切于 C 点, 圆弧轨道不会与其他轨道重合, A、B、C、D 均在同一竖直面内。质量 m=2kg 的小球 (可视为质点) 压紧轻质弹簧并被锁定, 解锁后小球以 Vo=4 m/s 的速度沿 AB 方向进入倾斜轨道滑下。已知轨道 AB 长 L=6m, 与水平方向夹角 θ = 37°。小球与轨道 AB、BC 间的动摩擦因数均为 μ=0.5。sin 37° = 0.6, cos 37° = 0.8。求:
**Sub-questions:**
(1) 未解锁时弹簧的弹性势能。
(2) 小球在 AB 轨道上运动的加速度大小 a。
(3) 小球在 A 点和 B 点时的速度大小 Vᴀ、Vʙ。
(4) 要使小球能够进入圆弧轨道且不脱离圆轨道, BC 轨道长度 d 应满足什么条件。
**Given Parameters/Constants:**
Radius of circular arc CD: R = 0.5 m
Mass of the small ball: m = 2 kg
Initial velocity along AB from A: V₀ = 4 m/s
Length of track AB: L = 6 m
Angle between AB and horizontal: θ = 37°
Coefficient of kinetic friction between ball and tracks AB, BC: μ = 0.5
sin 37° = 0.6
cos 37° = 0.8
**Diagram Description:**
* **Type:** Schematic diagram showing a mechanical system of tracks.
* **Main Elements:**
* An inclined straight track labeled AB, sloping upwards from A to B.
* A horizontal straight track labeled BC.
* A quarter-circular track labeled CD, tangent to BC at C and extending downwards to D. D is the lowest point of the circle.
* Points A, B, C, D are marked on the tracks. C is the connection point between BC and CD.
* A symbol representing a spring is shown at the left end of track AB, near point A.
* A circle represents the small ball.
* An arrow originating from A indicates the initial velocity V₀ along the direction of AB.
* The circular track CD has its center and radius R indicated. The center appears to be below BC and to the right of C.
* Labels for lengths and radius: L is shown near AB, d is shown near BC, R is shown as the radius of CD.
* An angle θ is indicated representing the inclination of AB with respect to the horizontal.
* **Relative Position and Direction:** Track AB is inclined. Track BC is horizontal. Track CD is a downward curve. AB is connected to BC via a small arc (not explicitly drawn but mentioned in text). BC is tangent to the circular track CD at C. The ball starts at A and moves towards B, then to C, then into the circular track towards D.
* **Legend:** None explicitly, labels are directly on the diagram.
**Handwritten Notes/Calculations:**
* v = mgh = 8J
* a = (mgsingθ - μmgcosθ) / m = 2m/s²
* vᴀ = v₀ = 4m/s
* (4).