| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Motion with applied force on slope |
| Difficulty | Standard +0.3 This is a straightforward M3 mechanics question requiring application of Hooke's Law and Newton's second law on a slope. Students must find extension (0.2m), calculate tension using T=λx/l (6N), resolve weight component (3.6N), then apply F=ma. All steps are standard procedures with no novel insight required, making it slightly easier than average. |
| Spec | 3.03u Static equilibrium: on rough surfaces |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(T = \frac{\Delta x}{l} = \frac{30-0.2}{1} = 6\) N | M1 A1 | |
| (b) Resolve \(\uparrow\): \(T - mg \sin \alpha = ma\) | M1 A1 | |
| \(\sin \alpha = \frac{3}{5}\) | M1 | |
| \(\therefore 6 - 0.6 \times 9.8 \times \frac{3}{5} = 0.6a\) | M1 | |
| giving \(a = 4.12\) ms\(^{-2}\) | A1 | (7) |
(a) $T = \frac{\Delta x}{l} = \frac{30-0.2}{1} = 6$ N | M1 A1
(b) Resolve $\uparrow$: $T - mg \sin \alpha = ma$ | M1 A1
$\sin \alpha = \frac{3}{5}$ | M1
$\therefore 6 - 0.6 \times 9.8 \times \frac{3}{5} = 0.6a$ | M1
giving $a = 4.12$ ms$^{-2}$ | A1 | (7)
---1.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{8b85b908-bb74-4532-a1b4-3826946bd43b-2_341_652_217_621}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{center}
\end{figure}
A particle of mass 0.6 kg is attached to one end of a light elastic spring of natural length 1 m and modulus of elasticity 30 N . The other end of the spring is fixed to a point $O$ which lies on a smooth plane inclined at an angle $\alpha$ to the horizontal where $\tan \alpha = \frac { 3 } { 4 }$ as shown in Figure 1.
The particle is held at rest on the slope at a point 1.2 m from $O$ down the line of greatest slope of the plane.
\begin{enumerate}[label=(\alph*)]
\item Find the tension in the spring.
\item Find the initial acceleration of the particle.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 Q1 [7]}}