Problem

1.

A particle of mass $2.5\,\mathrm{kg}$ moves on a smooth horizontal plane under the action of three horizontal forces, $\mathbf{F}_1$, $\mathbf{F}_2$ and $\mathbf{F}_3$, where

$$\mathbf{F}_1=(6\mathbf{i}+8\mathbf{j})\,\mathrm{N}$$ $$\mathbf{F}_2=(-16\mathbf{i}+2\mathbf{j})\,\mathrm{N}$$ $$\mathbf{F}_3=(-2\mathbf{i}+8\mathbf{j})\,\mathrm{N}$$

(a) Find the magnitude of the acceleration of the particle.

A fourth force, $\mathbf{F}_4=(p\mathbf{i}+p\mathbf{j})\,\mathrm{N}$, where $p$ is a constant, is added.

The resultant of the four forces acts in a direction that is parallel to the vector $(7\mathbf{i}+2\mathbf{j})$.

(b) Find the value of $p$.

题目勘误

官方原题：Q1(b) 前的条件写为 “in the direction of the vector $(7\mathbf{i}+2\mathbf{j})$”，即与该向量同方向。

实际上应为：“in a direction that is parallel to the vector $(7\mathbf{i}+2\mathbf{j})$”，即与该向量平行，不要求同方向。

Pearson 随卷附有 Clarification Notice，明确要求作上述更正。本页英文题面及中文翻译均已采用官方更正后的版本。