题目

Problem

A particle of mass $2\text{ kg}$ is attached to one end of a light inextensible string of length $0.6\text{ m}$ . The other end of the string is attached to a fixed point on a smooth horizontal surface. The particle is moving in a circular path on the surface. The tension in the string is $20\text{ N}$ .

Find how many revolutions the particle makes per minute.

(3)

题目中文翻译

一个质量为 $2\text{ kg}$ 的质点连接在一根长 $0.6\text{ m}$ 的轻质不可伸长细绳的一端。细绳的另一端连接在光滑水平面上的一个固定点。质点在该平面上沿圆周运动。细绳中的张力为 $20\text{ N}$ 。

求质点每分钟转动的圈数。

(3)

原卷通用作答要求

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

Where a numerical value for the acceleration due to gravity ( $g$ ) is needed, use $10\,\mathrm{m\,s^{-2}}$ .

需要使用重力加速度 $g$ 的数值时，取 $10\,\mathrm{m\,s^{-2}}$ 。

解答

解法一

思路

展开

张力提供向心力。求角速率后，用每圈 $2\pi$ 弧度和每分钟 $60$ 秒换算。

答题过程

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With radius $0.6\,\mathrm{m}$ , the radial equation is

\begin{align*} 20=&\,2(0.6)\omega^2,\\[4mm] \omega^2=&\,\frac{20}{1.2}=\frac{50}{3}. \end{align*}

The number of revolutions per minute is

\frac{60}{2\pi}\sqrt{\frac{50}{3}}=38.9848\ldots,

which is $39.0$ to three significant figures.

CIE 9231 2022 November Paper 31 Q1

题目

解答

解法一

思路

答题过程