Edexcel M1 2003 November — Question 3 9 marks

Exam BoardEdexcel
ModuleM1 (Mechanics 1)
Year2003
SessionNovember
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicForces, equilibrium and resultants
TypeEquilibrium with friction on horizontal surface
DifficultyStandard +0.3 This is a standard M1 equilibrium problem requiring resolution of forces in two directions, use of F=μR, and solving simultaneous equations. While it involves multiple steps (resolving horizontally and vertically, friction law, algebra), these are routine techniques practiced extensively in M1. The 30° angle and coefficient of 3/4 make the arithmetic straightforward. This is slightly easier than average as it follows a standard template with no conceptual surprises.
Spec3.03e Resolve forces: two dimensions3.03t Coefficient of friction: F <= mu*R model3.03v Motion on rough surface: including inclined planes

\includegraphics{figure_1} A heavy suitcase \(S\) of mass 50 kg is moving along a horizontal floor under the action of a force of magnitude \(P\) newtons. The force acts at 30° to the floor, as shown in Fig. 1, and \(S\) moves in a straight line at constant speed. The suitcase is modelled as a particle and the floor as a rough horizontal plane. The coefficient of friction between \(S\) and the floor is \(\frac{3}{4}\). Calculate the value of \(P\). [9]

AnswerMarks Guidance
\(R \uparrow: R = 50g + P \sin 30°\)M1 A2, 1, 0
\(R \rightarrow: F = P \cos 30°\)M1 A1
\(F = \frac{3}{5} R\) usedM1
\(P \cos 30° = \frac{3}{5}(50g + P \sin 30°)\) Elim \(F, R\)
Solve \(P = 520\) or \(519\) NM1 A1
Total: 9 marks
$R \uparrow: R = 50g + P \sin 30°$ | M1 | A2, 1, 0
$R \rightarrow: F = P \cos 30°$ | M1 | A1
$F = \frac{3}{5} R$ used | M1 |
$P \cos 30° = \frac{3}{5}(50g + P \sin 30°)$ Elim $F, R$ | |
Solve $P = 520$ or $519$ N | M1 | A1

**Total: 9 marks**

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\includegraphics{figure_1}

A heavy suitcase $S$ of mass 50 kg is moving along a horizontal floor under the action of a force of magnitude $P$ newtons. The force acts at 30° to the floor, as shown in Fig. 1, and $S$ moves in a straight line at constant speed. The suitcase is modelled as a particle and the floor as a rough horizontal plane. The coefficient of friction between $S$ and the floor is $\frac{3}{4}$.

Calculate the value of $P$. [9]

\hfill \mbox{\textit{Edexcel M1 2003 Q3 [9]}}