问题： （1） 若不启动电动机，玩具车以多大的初速度从 A 点弹出，恰好能沿轨道自行滑到 C 点？ （1） 如果电机没有启动，玩具车必须从 A 点启动的初始速度是多少，才能沿着轨道滑到 C 点？ (2) 玩具车以恒定功率 P=10 W 从 A 点由静止启动，电动机至少工作多长时间才能完成完整的圆周运动?并求此种情况下玩具车的停止点 I 与 F 点的距离。 （2） 如果玩具车从 A 点的静止位置启动，电机以恒定功率 P=10 W 工作，那么电机完成一个完整的圆周运动所需的最短工作时间是多少？并找到在这种情况下，停止点 I 和点 F 之间的距离。---**Question Number and Points:** 17. (10分) **Problem Stem:** 如图所示为遥控玩具小车比赛轨道的示意图，第一部分由斜面轨道 AB、圆弧轨道 BCD 与斜面轨道 DE 拼接而成, 圆弧 BCD 的圆心恰在 O 点, 第二部分由水平轨道 EF、圆形轨道 FGH 与特殊材料制成的水平轨道 FH 组成, 斜面轨道 DE 与水平轨道 EF 平滑连接, 直线轨道与圆轨道相切, 圆轨道 F 处前后略有错开, 小车可从一侧滑上再从另一侧滑出。已知轨道 AB 与 DE 的倾角均为 θ=37°, 长度均为 L=2m, 轨道 FGF 的半径 r=1m, 玩具车可视为质点, 在 AB 与 DE 轨道上受到的摩擦阻力为支持力的 1/4, 在 FH 轨道上受到的阻力为支持力的 1.5 倍, 其余轨道摩擦阻力及空气阻力均不计。已知玩具车输出功率恒为 P=10W, 电动机工作时间可调控, 玩具车质量 m=1kg。sin37°=0.6, cos37°=0.8, g取 10m/s²。 **Diagram Description:** Type: Schematic diagram of a toy car race track. Main Elements: - The track is composed of several sections: an inclined plane AB, a curved section BCD, an inclined plane DE, a horizontal section EF, a circular loop section FGH, and a horizontal section FI. - Points are labeled: A, B, C, D, E, F, G, H, I, and O. - AB and DE are straight inclined segments with angle θ relative to the horizontal. Both have length L. - BCD is a circular arc with center O. Point C is the lowest point of the arc. O is located on the horizontal line passing through A, E, F, I. - DE is smoothly connected to the horizontal track EF. - FGH is a circular loop (or part of a loop) with radius r. A point below FGH is indicated as the center for radius r. G is the highest point of the loop. - EF, FI are straight horizontal segments. - The horizontal line passing through A, O, E, F, I is indicated. - A toy car is depicted on the AB segment. - Angles: The inclination angle of AB and DE is labeled as θ=37°. - Lengths: The length of AB and DE is labeled as L. - Radius: The radius of the circular section "FGF" (presumably FGH) is labeled as r. - The center of the circular arc BCD is labeled as O. - Dashed lines are used to indicate the position of O and the center of the FGH loop, and to show the angle θ. **Given Data/Parameters:** - Inclination angle of AB and DE: θ = 37° - Length of AB and DE: L = 2m - Radius of circular track FGH (referred to as FGF): r = 1m - Toy car mass: m = 1kg - Friction on AB and DE: f_1 = (1/4) * Normal Force (N1) - Friction on FH (presumably FI? Or the horizontal section after the loop): f_2 = 1.5 * Normal Force (N2) - Friction and air resistance on BCD, EF, FGH: Negligible (均不计) - Motor output power: P = 10W (constant) - Motor work time: Adjustable - sin37° = 0.6 - cos37° = 0.8 - Acceleration due to gravity: g = 10m/s² **Questions:** (1) 若不启动电动机，玩具车以多大的初速度从 A 点弹出，恰好能沿轨道自行滑到 C 点? (1) If the motor is not started, what is the initial velocity the toy car must be launched with from point A so that it can just slide down the track to point C? (2) 玩具车以恒定功率 P=10 W 从 A 点由静止启动，电动机至少工作多长时间才能完成完整的圆周运动? 并求此种情况下玩具车的停止点 I 与 F 点的距离。 (2) If the toy car starts from rest at point A with the motor working at a constant power P=10 W, what is the minimum time the motor needs to work for the car to complete a full circular motion? And find the distance between the stopping point I and point F in this case.