题目

Problem

Coplanar forces of magnitudes $45\,\mathrm{N}$ , $28\,\mathrm{N}$ , $72\,\mathrm{N}$ and $35\,\mathrm{N}$ act at a point in the directions shown in the diagram.

Find, in either order, the magnitude and direction of the resultant force.

(6)

题目中文翻译

大小分别为 $45\,\mathrm{N}$ 、 $28\,\mathrm{N}$ 、 $72\,\mathrm{N}$ 和 $35\,\mathrm{N}$ 的共面力沿图示方向作用于同一点。

求合力的大小和方向，求解顺序不限。

(6)

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

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先用图中70与50度推出35N力在负水平线下60度，再取右、上为正分解。

答题过程

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Take rightwards and upwards as positive. The $35\,\mathrm{N}$ force acts $60^\circ$ below the leftward horizontal, since $180^\circ-50^\circ-70^\circ=60^\circ$ .

The resultant components are

\begin{align*} R_x=&\,28\cos35^\circ+72\cos50^\circ-35\cos60^\circ\\[4mm] =&\,51.716965\ldots\text{ N}, \end{align*}

\begin{align*} R_y=&\,45+28\sin35^\circ-72\sin50^\circ\\[4mm] &\,\hspace{2pt}-35\sin60^\circ\\[4mm] =&\,-24.405949\ldots\text{ N}. \end{align*}

Thus

R=\sqrt{R_x^2+R_y^2}=57.186492\ldots\approx\boxed{57.2\text{ N}}.

The resultant acts rightwards and downwards. Its angle below the rightward horizontal is

\phi=\tan^{-1}\biggl(\frac{|R_y|}{R_x}\biggr) =25.263271\ldots^\circ\approx\boxed{25.3^\circ}.

CIE 9709 2025 November Paper 41 Q3

题目

解答

解法一

思路

答题过程