| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2007 |
| Session | January |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Motion with applied force on slope |
| Difficulty | Moderate -0.3 This is a standard M1 mechanics problem involving resolving forces, friction, and Newton's second law. Part (a) requires resolving vertically and horizontally with constant velocity (equilibrium), then using F=μR. Part (b) applies F=ma with the new tension. While it requires careful setup and multiple steps (8+6 marks), it follows a completely standard template taught in every M1 course with no novel problem-solving required. |
| Spec | 3.03c Newton's second law: F=ma one dimension3.03e Resolve forces: two dimensions3.03r Friction: concept and vector form3.03s Contact force components: normal and frictional3.03t Coefficient of friction: F <= mu*R model3.03v Motion on rough surface: including inclined planes |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Use of \(F = μR\) | B1 | \(P \cos 20° = μR\) and \(R + P \sin 20° = 30g\) |
| (b) (i) \(R + 150 \sin 20° = 30g\) (\(R ≈ 242.7\)) | M1 A1 | (N2L) \(150 \cos 20° - μR = 30a\) |
**(a)** Use of $F = μR$ | B1 | $P \cos 20° = μR$ and $R + P \sin 20° = 30g$ | M1 A1 | $P \cos 20° = μ(30g - P \sin 20°)$ | M1 | $P = \frac{0.4 \times 30g}{\cos 20° + 0.4 \sin 20°}$ | M1 | $≈ 110$ (N) | A1 | accept 109 | 8 marks
**(b)** (i) $R + 150 \sin 20° = 30g$ ($R ≈ 242.7$) | M1 A1 | (N2L) $150 \cos 20° - μR = 30a$ | M1 A1 | $a ≈ \frac{150 \cos 20° - 0.4 \times 242.7}{30}$ | M1 | $= 1.5$ (m s$^{-2}$) | A1 | accept 1.46 | 6 marks | 14 marks total
---\includegraphics{figure_3}
A box of mass 30 kg is being pulled along rough horizontal ground at a constant speed using a rope. The rope makes an angle of 20° with the ground, as shown in Figure 3. The coefficient of friction between the box and the ground is 0.4. The box is modelled as a particle and the rope as a light, inextensible string. The tension in the rope is $P$ newtons.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $P$. [8]
\end{enumerate}
The tension in the rope is now increased to 150 N.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the acceleration of the box. [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2007 Q6 [14]}}