Edexcel M1 2003 January — Question 5 10 marks

Exam BoardEdexcel
ModuleM1 (Mechanics 1)
Year2003
SessionJanuary
Marks10
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicFriction
TypeParticle on inclined plane - force at angle to slope
DifficultyStandard +0.3 This is a standard M1 equilibrium problem requiring resolution of forces in two directions (parallel and perpendicular to the plane) with limiting friction. While it involves multiple forces and careful angle work, it follows a completely routine method taught extensively in M1: resolve perpendicular to find normal reaction, calculate friction force, then resolve parallel to find tension. The 10 marks reflect the working required rather than conceptual difficulty.
Spec3.03e Resolve forces: two dimensions3.03m Equilibrium: sum of resolved forces = 03.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces

\includegraphics{figure_1} A box of mass 1.5 kg is placed on a plane which is inclined at an angle of 30° to the horizontal. The coefficient of friction between the box and plane is \(\frac{1}{4}\). The box is kept in equilibrium by a light string which lies in a vertical plane containing a line of greatest slope of the plane. The string makes an angle of 20° with the plane, as shown in Fig. 2. The box is in limiting equilibrium and is about to move up the plane. The tension in the string is \(T\) newtons. The box is modelled as a particle. Find the value of \(T\). [10]

AnswerMarks
\(R(\angle): T \cos 20° = F + 1.5g \sin 30°\)M1 A2,1,0
\(R(↓): T \sin 20° + R = 1.5g \cos 30°\)M1 A2,1,0
Using \(F = \frac{1}{3}R\)M1
Eliminating \(R\), solve \(T\)M1, M1
\(T = 11\) or \(11.0\) NA1
Total: 10 marks
$R(\angle): T \cos 20° = F + 1.5g \sin 30°$ | M1 A2,1,0 |

$R(↓): T \sin 20° + R = 1.5g \cos 30°$ | M1 A2,1,0 |

Using $F = \frac{1}{3}R$ | M1 |

Eliminating $R$, solve $T$ | M1, M1 |

$T = 11$ or $11.0$ N | A1 |

**Total: 10 marks**

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\includegraphics{figure_1}

A box of mass 1.5 kg is placed on a plane which is inclined at an angle of 30° to the horizontal. The coefficient of friction between the box and plane is $\frac{1}{4}$. The box is kept in equilibrium by a light string which lies in a vertical plane containing a line of greatest slope of the plane. The string makes an angle of 20° with the plane, as shown in Fig. 2. The box is in limiting equilibrium and is about to move up the plane. The tension in the string is $T$ newtons. The box is modelled as a particle.

Find the value of $T$. [10]

\hfill \mbox{\textit{Edexcel M1 2003 Q5 [10]}}