Year 13 CAIE Physics Unit Test Mock Paper Walkthrough | CAIE 物理单元测试模拟卷解析

📚 Year 13 CAIE Physics Unit Test Mock Paper Walkthrough | CAIE 物理单元测试模拟卷解析

This mock paper targets the A2 unit on circular motion and gravitational fields, closely aligned with the CAIE 9702 syllabus. Each question is followed by a detailed bilingual solution designed to reinforce core concepts, equations, and exam technique. Work through every step to deepen your understanding.

本套模拟卷针对 A2 圆周运动与引力场单元，紧扣 CAIE 9702 考纲。每道题后都配有详细的双语解析，旨在巩固核心概念、公式及应试技巧。建议逐题演算，深入理解每一步推理。

1. Question 1: Centripetal Acceleration Direction | 第1题：向心加速度方向

A car moves at constant speed around a circular track. Which statement about its acceleration is correct? A. Zero acceleration. B. Acceleration directed toward the centre of the circle. C. Acceleration directed tangent to the circle. D. Acceleration directed away from the centre.

一辆汽车以恒定速率绕圆形赛道行驶。关于其加速度，哪项表述正确？A. 加速度为零。B. 加速度指向圆心。C. 加速度沿切线方向。D. 加速度背离圆心。

Answer: B

答案：B

In uniform circular motion the speed is constant, but the velocity vector changes direction continuously. This requires an acceleration directed toward the centre, known as centripetal acceleration. There is no change in the magnitude of velocity, so tangential acceleration is zero.

在匀速圆周运动中，速率恒定，但速度矢量方向持续改变。因此需要一个始终指向圆心的加速度，即向心加速度。由于速度大小不变，切向加速度为零。

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2. Question 2: Linear Speed from Period and Radius | 第2题：由周期和半径求线速度

A particle moves in a circle of radius 0.50 m with a constant period of 2.0 s. What is its linear speed? A. 0.79 m s⁻¹ B. 1.57 m s⁻¹ C. 3.14 m s⁻¹ D. 6.28 m s⁻¹

一质点沿半径为 0.50 m 的圆做匀速圆周运动，周期为 2.0 s。其线速度是多少？A. 0.79 m s⁻¹ B. 1.57 m s⁻¹ C. 3.14 m s⁻¹ D. 6.28 m s⁻¹

Answer: B

答案：B

The distance travelled in one period is the circumference 2πr. Hence, v = 2πr / T. Substituting r = 0.50 m and T = 2.0 s gives v = (2π × 0.50) / 2.0 = 0.50π ≈ 1.57 m s⁻¹.

一个周期内通过的路程为圆周长 2πr，因此 v = 2πr / T。代入 r = 0.50 m，T = 2.0 s，得 v = (2π × 0.50) / 2.0 = 0.50π ≈ 1.57 m s⁻¹。

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3. Question 3: Conical Pendulum Period | 第3题：圆锥摆周期

A conical pendulum consists of a bob of mass m attached to a light string of length L. The bob moves in a horizontal circle with constant speed, and the string makes an angle θ to the vertical. Which expression gives the period T of the bob’s motion?

一个圆锥摆由质量为 m 的小球和一根长为 L 的轻绳构成。小球在水平面内做匀速圆周运动，绳与竖直方向的夹角为 θ。下列哪个表达式给出了小球的运动周期 T？

A. T = 2π√(L sinθ / g) B. T = 2π√(L cosθ / g) C. T = 2π√(L / g) D. T = 2π√(L tanθ / g)

Answer: B

答案：B

Resolving forces: vertically, T cosθ = mg. Horizontally, T sinθ = mω²r, where r = L sinθ. Dividing these equations gives ω² = g / (L cosθ). Since T = 2π/ω, we obtain T = 2π√(L cosθ / g).

受力分析：竖直方向 T cosθ = mg；水平方向 T sinθ = mω²r，而 r = L sinθ。两式相除可得 ω² = g / (L cosθ)。由 T = 2π/ω，最终得到 T = 2π√(L cosθ / g)。

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4. Question 4: Roller Coaster at the Top of a Loop | 第4题：过山车环顶端运动

A roller coaster car of mass 500 kg enters a vertical circular loop of radius 8.0 m. What is the minimum speed at the top of the loop for the car to stay on the track? (Take g = 9.8 m s⁻²) A. 8.9 m s⁻¹ B. 12.5 m s⁻¹ C. 6.3 m s⁻¹ D. 4.0 m s⁻¹

一辆质量为 500 kg 的过山车进入半径为 8.0 m 的竖直圆环。车在环顶端不脱离轨道的最小速度是多少？(取 g = 9.8 m s⁻²) A. 8.9 m s⁻¹ B. 12.5 m s⁻¹ C. 6.3 m s⁻¹ D. 4.0 m s⁻¹

Answer: A

答案：A

At the top, the centripetal force equals the sum of the weight and the normal reaction. For minimum speed, the normal force N = 0, so mg = mv²/r. Hence, v = √(gr) = √(9.8 × 8.0) ≈ 8.85 m s⁻¹, which rounds to 8.9 m s⁻¹.

在环顶端，向心力等于重力与正压力的合力。最小速度对应正压力 N = 0，此时 mg = mv²/r，故 v = √(gr) = √(9.8 × 8.0) ≈ 8.85 m s⁻¹，约为 8.9 m s⁻¹。

If the speed is 12 m s⁻¹, calculate the normal contact force. Substituting v = 12 m s⁻¹ into N = mv²/r – mg gives N = (500 × 12² / 8.0) – (500 × 9.8) = 9000 – 4900 = 4100 N.

若速度为 12 m s⁻¹，计算正压力。代入公式 N = mv²/r – mg，得 N = (500 × 12² / 8.0) – (500 × 9.8) = 9000 – 4900 = 4100 N。

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5. Question 5: Car Turning on a Flat Road | 第5题：平路汽车转弯

A car of mass 1200 kg travels around a bend of radius 50 m on a flat road. The coefficient of static friction between the tyres and the road is 0.60. What is the maximum safe speed without skidding? (g = 9.8 m s⁻²) A. 17 m s⁻¹ B.

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