| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Modelling assumptions and refinements |
| Difficulty | Moderate -0.8 This is a straightforward M1 mechanics question requiring a force diagram, resolving forces in two directions (parallel and perpendicular to slope), and discussing basic modelling assumptions. The calculations are routine (resolving with sin/cos of 25°), and the modelling discussion requires only standard textbook responses about particles, light inextensible strings, and the effect of friction. No problem-solving insight or novel application is needed. |
| Spec | 3.03e Resolve forces: two dimensions3.03f Weight: W=mg3.03m Equilibrium: sum of resolved forces = 03.03n Equilibrium in 2D: particle under forces |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Reaction \(20 \text{ N}\) at angle shown with Weight | B2 | |
| (b) resolve // to plane: \(20 - W\sin 25° = 0\) | M1 | |
| \(W = \frac{20}{\sin 25°}\) so \(W = 47.3 \text{ N}\) (3sf) | A1 | |
| resolve perp. to plane: \(R - W\cos 25° = 0\) | M1 | |
| \(R = 47.324 \times \cos 25° = 42.9 \text{ N}\) (3sf) | A1 | |
| (c) (i) particle | B1 | |
| (ii) inextensible | B1 | |
| (d) \(W\) and \(R\) will both be lower | B2 | (10) |
**(a)** Reaction $20 \text{ N}$ at angle shown with Weight | B2 |
**(b)** resolve // to plane: $20 - W\sin 25° = 0$ | M1 |
$W = \frac{20}{\sin 25°}$ so $W = 47.3 \text{ N}$ (3sf) | A1 |
resolve perp. to plane: $R - W\cos 25° = 0$ | M1 |
$R = 47.324 \times \cos 25° = 42.9 \text{ N}$ (3sf) | A1 |
**(c)** (i) particle | B1 |
(ii) inextensible | B1 |
**(d)** $W$ and $R$ will both be lower | B2 | (10)2.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{10b4d660-3980-4204-b18d-5240dea61a45-2_321_666_584_534}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{center}
\end{figure}
Figure 1 shows a toy lorry being pulled by a piece of string, up a ramp inclined at an angle of $25 ^ { \circ }$ to the horizontal. When the string is pulled with a force of 20 N parallel to the line of greatest slope of the ramp, the lorry is on the point of moving up the ramp.
In a simple model of the situation, the ramp is considered to be smooth.
\begin{enumerate}[label=(\alph*)]
\item Draw a diagram showing all the forces acting on the lorry.
\item Find the weight of the lorry and the magnitude of the reaction between the lorry and the ramp, giving your answers to an appropriate degree of accuracy.
\item Write down any modelling assumptions that you have made about
\begin{enumerate}[label=(\roman*)]
\item the lorry,
\item the string.
In a more refined model, the ramp is assumed to be rough.
\end{enumerate}\item State the effect that this would have on your answers to part (b).
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q2 [10]}}