Edexcel M1 2009 June — Question 4 9 marks

Exam BoardEdexcel
ModuleM1 (Mechanics 1)
Year2009
SessionJune
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMotion on a slope
TypeMotion down rough slope
DifficultyStandard +0.3 This is a standard M1 inclined plane problem requiring resolution of forces, friction calculation, and Newton's second law. While it involves multiple steps (finding sin θ and cos θ from tan θ, resolving perpendicular for normal reaction, calculating friction, resolving parallel, applying F=ma), these are all routine procedures that follow a well-practiced method with no novel insight required. Slightly above average difficulty due to the multi-step nature and need for careful trigonometry.
Spec3.03a Force: vector nature and diagrams3.03b Newton's first law: equilibrium3.03c Newton's second law: F=ma one dimension3.03e Resolve forces: two dimensions3.03f Weight: W=mg3.03i Normal reaction force3.03r Friction: concept and vector form3.03t Coefficient of friction: F <= mu*R model3.03v Motion on rough surface: including inclined planes

A small brick of mass 0.5 kg is placed on a rough plane which is inclined to the horizontal at an angle \(\theta\), where \(\tan \theta = \frac{4}{3}\), and released from rest. The coefficient of friction between the brick and the plane is \(\frac{1}{3}\). Find the acceleration of the brick. [9]

AnswerMarks
\(0.5g\sin\theta - F = 0.5a\)M1 A1 A1
\(F = \frac{1}{3}R\) seenB1
\(R = 0.5g\cos\theta\)M1 A1
Use of \(\sin\theta = \frac{4}{5}\) or \(\cos\theta = \frac{3}{5}\) or decimal equiv or decimal angle e.g. \(53.1°\) or \(53°\)B1
\(a = \frac{3g}{5}\) or \(5.88 \text{ m s}^{-2}\) or \(5.9 \text{ m s}^{-2}\)DM1 A1
Total: [9]
$0.5g\sin\theta - F = 0.5a$ | M1 A1 A1 |
$F = \frac{1}{3}R$ seen | B1 |
$R = 0.5g\cos\theta$ | M1 A1 |
Use of $\sin\theta = \frac{4}{5}$ or $\cos\theta = \frac{3}{5}$ or decimal equiv or decimal angle e.g. $53.1°$ or $53°$ | B1 |
$a = \frac{3g}{5}$ or $5.88 \text{ m s}^{-2}$ or $5.9 \text{ m s}^{-2}$ | DM1 A1 |
| **Total: [9]** |
A small brick of mass 0.5 kg is placed on a rough plane which is inclined to the horizontal at an angle $\theta$, where $\tan \theta = \frac{4}{3}$, and released from rest. The coefficient of friction between the brick and the plane is $\frac{1}{3}$.

Find the acceleration of the brick. [9]

\hfill \mbox{\textit{Edexcel M1 2009 Q4 [9]}}