\includegraphics{figure_2} A small packet of mass 0.3 kg rests on a rough horizontal surface. The coefficient of friction between the packet and the surface is \(\frac{1}{4}\). Two strings are attached to the packet, making angles of 45° and 30° with the horizontal, and when forces of magnitude 2 N and \(F\) N are exerted through the strings as shown, the packet is on the point of moving in the direction \(\overrightarrow{AB}\). Find the value of \(F\). \hfill [7 marks]

Resolve horizontally: $F \cos 30° = 2 \cos 45° + 0.25R$ | M1 A1 |

Resolve vertically: $R + 2 \sin 45° + F \sin 30° = 0.3g$ | M1 A1 |

$0.866F = 1.414 + 0.25(0.3g - 1.414 - 0.5F)$ | M1 A1 |

$0.991F = 1.796$ → $F = 1.81$ | A1 | **Total: 7 marks**

\includegraphics{figure_2}

A small packet of mass 0.3 kg rests on a rough horizontal surface. The coefficient of friction between the packet and the surface is $\frac{1}{4}$. Two strings are attached to the packet, making angles of 45° and 30° with the horizontal, and when forces of magnitude 2 N and $F$ N are exerted through the strings as shown, the packet is on the point of moving in the direction $\overrightarrow{AB}$.

Find the value of $F$. \hfill [7 marks]

\hfill \mbox{\textit{Edexcel M1  Q2 [7]}}